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


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


















2












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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.






limits







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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.















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
















2












2








2


2



$begingroup$



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.






limits







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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




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.














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




















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


















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






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












1 Answer
1






active

oldest

votes


















1












$begingroup$

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










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










  • $begingroup$
    Ok thanks I will try
    $endgroup$
    – 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












$begingroup$

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









$endgroup$













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










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










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
















1












$begingroup$

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









$endgroup$













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










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










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














1












1








1





$begingroup$

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









$endgroup$



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

62.9k24090




62.9k24090












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










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










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


















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










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










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
















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




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












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




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












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




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



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