Use sigma notation to write the sum -1+2+7+14+23+…+62. [on hold]

-2

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.

edited Jan 4 at 7:16

JimmyK4542

40.5k245105

asked Jan 4 at 7:09

Nick29

New contributor

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 |

-2

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.

edited Jan 4 at 7:16

JimmyK4542

40.5k245105

asked Jan 4 at 7:09

Nick29

New contributor

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 |

-2

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.

edited Jan 4 at 7:16

JimmyK4542

40.5k245105

asked Jan 4 at 7:09

Nick29

New contributor

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

Nick29

New contributor

edited Jan 4 at 7:16

JimmyK4542

40.5k245105

asked Jan 4 at 7:09

Nick29

New contributor

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

asked Jan 4 at 7:09

Nick29

New contributor

asked Jan 4 at 7:09

Nick29

asked Jan 4 at 7:09

Nick29

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.

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

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

Arthur

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 Parkinson

9159

New contributor

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

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

Arthur

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

Arthur

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

Arthur

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

Arthur

111k7105186

answered Jan 4 at 7:15

Arthur

111k7105186

answered Jan 4 at 7:15

Arthur

111k7105186

answered Jan 4 at 7:15

Arthur

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 Parkinson

9159

New contributor

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 Parkinson

9159

New contributor

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 Parkinson

9159

New contributor

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 Parkinson

9159

New contributor

answered Jan 4 at 7:18

Erik Parkinson

9159

New contributor

answered Jan 4 at 7:18

Erik Parkinson

9159

answered Jan 4 at 7:18

Erik 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

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 |

This page is only for reference, If you need detailed information, please check here

搜尋此網誌

Mfrhtyj