Calculating $lim_{nto infty}{frac{frac{n}{1} + frac{n-1}{2} + frac{n-2}{3} + … + frac{2}{n-1} +...












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  • Compute $lim_{ntoinfty}frac{tfrac{n}{1}+tfrac{n-1}{2}+dots+tfrac{2}{n-1}+tfrac{1}{n}}{ln(n!)}$ [closed]

    2 answers




I have tried to use the Stolz theorem and calculate $lim_{nto infty}{frac{a_{n+1}-a_n}{b_{n+1}-b_n}}$ and i have reached $lim_{nto infty}{frac{1 + frac{1}{2} + frac{1}{3} + ... + frac{1}{n-2} + frac{1}{n-1} + frac{1}{n}}{ln (n+1)}}$ but I do not know how to continue. Could someone help me? Thanks in advance.










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marked as duplicate by A. Pongrácz, amWhy, RRL, jgon, Davide Giraudo Jan 4 at 21:59


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.















  • Where is this problem from? It has been asked a couple of days ago: math.stackexchange.com/questions/3055274/…
    – A. Pongrácz
    Jan 4 at 12:07


















2















This question already has an answer here:




  • Compute $lim_{ntoinfty}frac{tfrac{n}{1}+tfrac{n-1}{2}+dots+tfrac{2}{n-1}+tfrac{1}{n}}{ln(n!)}$ [closed]

    2 answers




I have tried to use the Stolz theorem and calculate $lim_{nto infty}{frac{a_{n+1}-a_n}{b_{n+1}-b_n}}$ and i have reached $lim_{nto infty}{frac{1 + frac{1}{2} + frac{1}{3} + ... + frac{1}{n-2} + frac{1}{n-1} + frac{1}{n}}{ln (n+1)}}$ but I do not know how to continue. Could someone help me? Thanks in advance.










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marked as duplicate by A. Pongrácz, amWhy, RRL, jgon, Davide Giraudo Jan 4 at 21:59


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.















  • Where is this problem from? It has been asked a couple of days ago: math.stackexchange.com/questions/3055274/…
    – A. Pongrácz
    Jan 4 at 12:07
















2












2








2


2






This question already has an answer here:




  • Compute $lim_{ntoinfty}frac{tfrac{n}{1}+tfrac{n-1}{2}+dots+tfrac{2}{n-1}+tfrac{1}{n}}{ln(n!)}$ [closed]

    2 answers




I have tried to use the Stolz theorem and calculate $lim_{nto infty}{frac{a_{n+1}-a_n}{b_{n+1}-b_n}}$ and i have reached $lim_{nto infty}{frac{1 + frac{1}{2} + frac{1}{3} + ... + frac{1}{n-2} + frac{1}{n-1} + frac{1}{n}}{ln (n+1)}}$ but I do not know how to continue. Could someone help me? Thanks in advance.










share|cite|improve this question














This question already has an answer here:




  • Compute $lim_{ntoinfty}frac{tfrac{n}{1}+tfrac{n-1}{2}+dots+tfrac{2}{n-1}+tfrac{1}{n}}{ln(n!)}$ [closed]

    2 answers




I have tried to use the Stolz theorem and calculate $lim_{nto infty}{frac{a_{n+1}-a_n}{b_{n+1}-b_n}}$ and i have reached $lim_{nto infty}{frac{1 + frac{1}{2} + frac{1}{3} + ... + frac{1}{n-2} + frac{1}{n-1} + frac{1}{n}}{ln (n+1)}}$ but I do not know how to continue. Could someone help me? Thanks in advance.





This question already has an answer here:




  • Compute $lim_{ntoinfty}frac{tfrac{n}{1}+tfrac{n-1}{2}+dots+tfrac{2}{n-1}+tfrac{1}{n}}{ln(n!)}$ [closed]

    2 answers








limits






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asked Jan 4 at 11:26









AndarrkorAndarrkor

446




446




marked as duplicate by A. Pongrácz, amWhy, RRL, jgon, Davide Giraudo Jan 4 at 21:59


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.






marked as duplicate by A. Pongrácz, amWhy, RRL, jgon, Davide Giraudo Jan 4 at 21:59


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.














  • Where is this problem from? It has been asked a couple of days ago: math.stackexchange.com/questions/3055274/…
    – A. Pongrácz
    Jan 4 at 12:07




















  • Where is this problem from? It has been asked a couple of days ago: math.stackexchange.com/questions/3055274/…
    – A. Pongrácz
    Jan 4 at 12:07


















Where is this problem from? It has been asked a couple of days ago: math.stackexchange.com/questions/3055274/…
– A. Pongrácz
Jan 4 at 12:07






Where is this problem from? It has been asked a couple of days ago: math.stackexchange.com/questions/3055274/…
– A. Pongrácz
Jan 4 at 12:07












1 Answer
1






active

oldest

votes


















1














Hint: See the "Rate of divergence" section of the Wikipedia article about the harmonic series, or the definition of the Euler-Mascheroni constant.






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  • So i can rewrite the top part as $ln(n) + gamma + frac{1}{2n}$?
    – Andarrkor
    Jan 4 at 11:42










  • No....but you can approximate it by that (or better still, find upper and lower bounds and use the squeeze lemma).
    – John Hughes
    Jan 4 at 13:26










  • Ok thanks I will try
    – Andarrkor
    Jan 4 at 13:31


















1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









1














Hint: See the "Rate of divergence" section of the Wikipedia article about the harmonic series, or the definition of the Euler-Mascheroni constant.






share|cite|improve this answer





















  • So i can rewrite the top part as $ln(n) + gamma + frac{1}{2n}$?
    – Andarrkor
    Jan 4 at 11:42










  • No....but you can approximate it by that (or better still, find upper and lower bounds and use the squeeze lemma).
    – John Hughes
    Jan 4 at 13:26










  • Ok thanks I will try
    – Andarrkor
    Jan 4 at 13:31
















1














Hint: See the "Rate of divergence" section of the Wikipedia article about the harmonic series, or the definition of the Euler-Mascheroni constant.






share|cite|improve this answer





















  • So i can rewrite the top part as $ln(n) + gamma + frac{1}{2n}$?
    – Andarrkor
    Jan 4 at 11:42










  • No....but you can approximate it by that (or better still, find upper and lower bounds and use the squeeze lemma).
    – John Hughes
    Jan 4 at 13:26










  • Ok thanks I will try
    – Andarrkor
    Jan 4 at 13:31














1












1








1






Hint: See the "Rate of divergence" section of the Wikipedia article about the harmonic series, or the definition of the Euler-Mascheroni constant.






share|cite|improve this answer












Hint: See the "Rate of divergence" section of the Wikipedia article about the harmonic series, or the definition of the Euler-Mascheroni constant.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Jan 4 at 11:32









John HughesJohn Hughes

62.6k24090




62.6k24090












  • So i can rewrite the top part as $ln(n) + gamma + frac{1}{2n}$?
    – Andarrkor
    Jan 4 at 11:42










  • No....but you can approximate it by that (or better still, find upper and lower bounds and use the squeeze lemma).
    – John Hughes
    Jan 4 at 13:26










  • Ok thanks I will try
    – Andarrkor
    Jan 4 at 13:31


















  • So i can rewrite the top part as $ln(n) + gamma + frac{1}{2n}$?
    – Andarrkor
    Jan 4 at 11:42










  • No....but you can approximate it by that (or better still, find upper and lower bounds and use the squeeze lemma).
    – John Hughes
    Jan 4 at 13:26










  • Ok thanks I will try
    – Andarrkor
    Jan 4 at 13:31
















So i can rewrite the top part as $ln(n) + gamma + frac{1}{2n}$?
– Andarrkor
Jan 4 at 11:42




So i can rewrite the top part as $ln(n) + gamma + frac{1}{2n}$?
– Andarrkor
Jan 4 at 11:42












No....but you can approximate it by that (or better still, find upper and lower bounds and use the squeeze lemma).
– John Hughes
Jan 4 at 13:26




No....but you can approximate it by that (or better still, find upper and lower bounds and use the squeeze lemma).
– John Hughes
Jan 4 at 13:26












Ok thanks I will try
– Andarrkor
Jan 4 at 13:31




Ok thanks I will try
– Andarrkor
Jan 4 at 13:31



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