There is no value of <em>c</em> such that the <em>infinite</em> series converges.
<h3>How to analyze the converge of an infinite series </h3>
Convergence is a characteristic of <em>infinite</em> series, in which a sum tends to be a given number when <em>n</em> tends to +∞.
In this question we must prove for which values of <em>c</em> the <em>infinite</em> series may converge.
There are different criteria to prove whether a given series converges or not, one of the most used criteria is the <em>ratio</em> criterion, which states that:
, where the series converges if and only if <em>r > 1</em>. (1)
If we know that , then the rational formula is:
We notice that resulting expression does not depend on <em>c</em> and is greater than 1. Therefore, there is no value of <em>c</em> such that the <em>infinite</em> series converges.
<h3>Remark</h3>
<em>If </em><em> is a positive real number and </em><em>, for what values of </em><em>, if any, does the infinite series </em><em> converge?</em>
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