Comments - Two Beautiful Mathematical Results - Data Science Central2020-08-09T05:35:26Zhttps://www.datasciencecentral.com/profiles/comment/feed?attachedTo=6448529%3ABlogPost%3A705889&xn_auth=noIt is worth mentioning that tâ€¦tag:www.datasciencecentral.com,2018-06-23:6448529:Comment:7355732018-06-23T01:27:33.922Zvictor zurkowskihttps://www.datasciencecentral.com/profile/victorzurkowski
<p>It is worth mentioning that the identity $\Sigma_{k=0}{\infty} x^{3k} = \frac{1}{1-x^3}$ and the term by term integration hold for $x \in (0,1)$. To justify the evaluation of the series at $ x= - 1$ still equals the value of the integral, one appeals to Abel's theorem.</p>
<p>It is worth mentioning that the identity $\Sigma_{k=0}{\infty} x^{3k} = \frac{1}{1-x^3}$ and the term by term integration hold for $x \in (0,1)$. To justify the evaluation of the series at $ x= - 1$ still equals the value of the integral, one appeals to Abel's theorem.</p>