Difference between revisions of "AoPS Wiki talk:Problem of the Day/August 3, 2011"

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{{:AoPSWiki:Problem of the Day/August 3, 2011}}
 
==Solution==
 
==Solution==
Since <math>\lim_{n \to \infty}\dfrac{5^n+n}{n} = +\infty</math>, the sum diverges.
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Since <math>\sum_{1 \to \infty}\dfrac{5^n+n}{n} = \sum_{1 \to \infty}\left(1+\frac{5^n}{n}\right)</math>, the sum diverges, since the sum is always greater than the index, due to constant 1.
  
 
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Revision as of 03:37, 18 August 2011

Problem

AoPSWiki:Problem of the Day/August 3, 2011

Solution

Since $\sum_{1 \to \infty}\dfrac{5^n+n}{n} = \sum_{1 \to \infty}\left(1+\frac{5^n}{n}\right)$, the sum diverges, since the sum is always greater than the index, due to constant 1.

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