Use sigma notation to write the sum -1+2+7+14+23+…+62. [on hold]
The series
$$
-1+2+7+14+23+...+62
$$
is neither algebraic nor geometric. However, I can't seem to figure out how to write it in sigma notation.
summation
edited Jan 4 at 7:16
JimmyK4542
40.5k245105
asked Jan 4 at 7:09
Nick29Nick29
81
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put on hold as off-topic by José Carlos Santos, Nosrati, Kavi Rama Murthy, Paul Frost, mrtaurho Jan 4 at 13:26
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – José Carlos Santos, Nosrati, Kavi Rama Murthy, Paul Frost, mrtaurho
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
The series
$$
-1+2+7+14+23+...+62
$$
is neither algebraic nor geometric. However, I can't seem to figure out how to write it in sigma notation.
summation
edited Jan 4 at 7:16
JimmyK4542
40.5k245105
asked Jan 4 at 7:09
Nick29Nick29
81
New contributor
Nick29 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by José Carlos Santos, Nosrati, Kavi Rama Murthy, Paul Frost, mrtaurho Jan 4 at 13:26
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – José Carlos Santos, Nosrati, Kavi Rama Murthy, Paul Frost, mrtaurho
If this question can be reworded to fit the rules in the help center, please edit the question.
Hey @Nick29 - Just so you are aware you need to provide some background/context to the problem and must show all attempts taken. If you are unable to start please state so in the question. Welcome to MSE btw!
– DavidG
Jan 4 at 7:21
2
consider a sequence of perfect squares.
– Doug M
Jan 4 at 7:23
add a comment |
The series
$$
-1+2+7+14+23+...+62
$$
is neither algebraic nor geometric. However, I can't seem to figure out how to write it in sigma notation.
summation
edited Jan 4 at 7:16
JimmyK4542
40.5k245105
asked Jan 4 at 7:09
Nick29Nick29
81
New contributor
Nick29 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
The series
$$
-1+2+7+14+23+...+62
$$
is neither algebraic nor geometric. However, I can't seem to figure out how to write it in sigma notation.
summation
summation
edited Jan 4 at 7:16
JimmyK4542
40.5k245105
asked Jan 4 at 7:09
Nick29Nick29
81
New contributor
Nick29 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Jan 4 at 7:16
JimmyK4542
40.5k245105
asked Jan 4 at 7:09
Nick29Nick29
81
New contributor
Nick29 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Jan 4 at 7:16
JimmyK4542
40.5k245105
edited Jan 4 at 7:16
JimmyK4542
40.5k245105
edited Jan 4 at 7:16
JimmyK4542
40.5k245105
40.5k245105
asked Jan 4 at 7:09
Nick29Nick29
81
New contributor
Nick29 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Jan 4 at 7:09
Nick29Nick29
81
asked Jan 4 at 7:09
Nick29Nick29
81
81
New contributor
Nick29 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Nick29 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Nick29 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by José Carlos Santos, Nosrati, Kavi Rama Murthy, Paul Frost, mrtaurho Jan 4 at 13:26
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – José Carlos Santos, Nosrati, Kavi Rama Murthy, Paul Frost, mrtaurho
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by José Carlos Santos, Nosrati, Kavi Rama Murthy, Paul Frost, mrtaurho Jan 4 at 13:26
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – José Carlos Santos, Nosrati, Kavi Rama Murthy, Paul Frost, mrtaurho
If this question can be reworded to fit the rules in the help center, please edit the question.
Hey @Nick29 - Just so you are aware you need to provide some background/context to the problem and must show all attempts taken. If you are unable to start please state so in the question. Welcome to MSE btw!
– DavidG
Jan 4 at 7:21
2
consider a sequence of perfect squares.
– Doug M
Jan 4 at 7:23
add a comment |
Hey @Nick29 - Just so you are aware you need to provide some background/context to the problem and must show all attempts taken. If you are unable to start please state so in the question. Welcome to MSE btw!
– DavidG
Jan 4 at 7:21
2
consider a sequence of perfect squares.
– Doug M
Jan 4 at 7:23
Hey @Nick29 - Just so you are aware you need to provide some background/context to the problem and must show all attempts taken. If you are unable to start please state so in the question. Welcome to MSE btw!
– DavidG
Jan 4 at 7:21
Hey @Nick29 - Just so you are aware you need to provide some background/context to the problem and must show all attempts taken. If you are unable to start please state so in the question. Welcome to MSE btw!
– DavidG
Jan 4 at 7:21
2
2
consider a sequence of perfect squares.
– Doug M
Jan 4 at 7:23
consider a sequence of perfect squares.
– Doug M
Jan 4 at 7:23
add a comment |
2 Answers
2
active
oldest
votes
Hint: Add $2$ to each term. Can you write that series using $sum$ notation?
Cheap solution: just write
$$
sum_{i=1}^1 (-1+2+7+cdots+62)
$$
answered Jan 4 at 7:15
ArthurArthur
111k7105186
add a comment |
The differences between the numbers in the series are $3,5,7,9,...$ which is linear. Therefore the series must be quadratic. The constant term must be $-1$ so it is of the form
$$sum_{i=0}^{}ai^2+bi-1$$
Looking at $i=1$ and $i=2$ gives $a+b-1=2$, $4a+2b-1=7$. Solving this gives $a=2$, $b=2$.
So the solution is
$$sum_{i=0}^{7}i^2+2i-1$$
answered Jan 4 at 7:18
Erik ParkinsonErik Parkinson
9159
New contributor
Erik Parkinson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
2
Starting at $i=1$ makes the expression a lot cleaner.
– Arthur
Jan 4 at 7:22
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
Hint: Add $2$ to each term. Can you write that series using $sum$ notation?
Cheap solution: just write
$$
sum_{i=1}^1 (-1+2+7+cdots+62)
$$
answered Jan 4 at 7:15
ArthurArthur
111k7105186
add a comment |
Hint: Add $2$ to each term. Can you write that series using $sum$ notation?
Cheap solution: just write
$$
sum_{i=1}^1 (-1+2+7+cdots+62)
$$
answered Jan 4 at 7:15
ArthurArthur
111k7105186
add a comment |
Hint: Add $2$ to each term. Can you write that series using $sum$ notation?
Cheap solution: just write
$$
sum_{i=1}^1 (-1+2+7+cdots+62)
$$
answered Jan 4 at 7:15
ArthurArthur
111k7105186
Hint: Add $2$ to each term. Can you write that series using $sum$ notation?
Cheap solution: just write
$$
sum_{i=1}^1 (-1+2+7+cdots+62)
$$
answered Jan 4 at 7:15
ArthurArthur
111k7105186
answered Jan 4 at 7:15
ArthurArthur
111k7105186
answered Jan 4 at 7:15
ArthurArthur
111k7105186
answered Jan 4 at 7:15
ArthurArthur
111k7105186
111k7105186
add a comment |
add a comment |
The differences between the numbers in the series are $3,5,7,9,...$ which is linear. Therefore the series must be quadratic. The constant term must be $-1$ so it is of the form
$$sum_{i=0}^{}ai^2+bi-1$$
Looking at $i=1$ and $i=2$ gives $a+b-1=2$, $4a+2b-1=7$. Solving this gives $a=2$, $b=2$.
So the solution is
$$sum_{i=0}^{7}i^2+2i-1$$
answered Jan 4 at 7:18
Erik ParkinsonErik Parkinson
9159
New contributor
Erik Parkinson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
2
Starting at $i=1$ makes the expression a lot cleaner.
– Arthur
Jan 4 at 7:22
add a comment |
The differences between the numbers in the series are $3,5,7,9,...$ which is linear. Therefore the series must be quadratic. The constant term must be $-1$ so it is of the form
$$sum_{i=0}^{}ai^2+bi-1$$
Looking at $i=1$ and $i=2$ gives $a+b-1=2$, $4a+2b-1=7$. Solving this gives $a=2$, $b=2$.
So the solution is
$$sum_{i=0}^{7}i^2+2i-1$$
answered Jan 4 at 7:18
Erik ParkinsonErik Parkinson
9159
New contributor
Erik Parkinson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
2
Starting at $i=1$ makes the expression a lot cleaner.
– Arthur
Jan 4 at 7:22
add a comment |
The differences between the numbers in the series are $3,5,7,9,...$ which is linear. Therefore the series must be quadratic. The constant term must be $-1$ so it is of the form
$$sum_{i=0}^{}ai^2+bi-1$$
Looking at $i=1$ and $i=2$ gives $a+b-1=2$, $4a+2b-1=7$. Solving this gives $a=2$, $b=2$.
So the solution is
$$sum_{i=0}^{7}i^2+2i-1$$
answered Jan 4 at 7:18
Erik ParkinsonErik Parkinson
9159
New contributor
Erik Parkinson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
The differences between the numbers in the series are $3,5,7,9,...$ which is linear. Therefore the series must be quadratic. The constant term must be $-1$ so it is of the form
$$sum_{i=0}^{}ai^2+bi-1$$
Looking at $i=1$ and $i=2$ gives $a+b-1=2$, $4a+2b-1=7$. Solving this gives $a=2$, $b=2$.
So the solution is
$$sum_{i=0}^{7}i^2+2i-1$$
answered Jan 4 at 7:18
Erik ParkinsonErik Parkinson
9159
New contributor
Erik Parkinson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered Jan 4 at 7:18
Erik ParkinsonErik Parkinson
9159
New contributor
Erik Parkinson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered Jan 4 at 7:18
Erik ParkinsonErik Parkinson
9159
answered Jan 4 at 7:18
Erik ParkinsonErik Parkinson
9159
9159
New contributor
Erik Parkinson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Erik Parkinson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Erik Parkinson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
2
Starting at $i=1$ makes the expression a lot cleaner.
– Arthur
Jan 4 at 7:22
add a comment |
2
Starting at $i=1$ makes the expression a lot cleaner.
– Arthur
Jan 4 at 7:22
2
2
Starting at $i=1$ makes the expression a lot cleaner.
– Arthur
Jan 4 at 7:22
Starting at $i=1$ makes the expression a lot cleaner.
– Arthur
Jan 4 at 7:22
add a comment |
Hey @Nick29 - Just so you are aware you need to provide some background/context to the problem and must show all attempts taken. If you are unable to start please state so in the question. Welcome to MSE btw!
– DavidG
Jan 4 at 7:21
2
consider a sequence of perfect squares.
– Doug M
Jan 4 at 7:23