1. Tardigrade
  2. Question
  3. Mathematics
  4. Let Sn=n-2015(1+22014+32014+ ldots +n2014), then reciprocal of undersetn arrow ∞ textLim Sn is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Let $S_{n}=n^{-2015}\left(1+2^{2014}+3^{2014}+\ldots +n^{2014}\right)$, then reciprocal of $\underset{n \rightarrow \infty}{\text{Lim}} S_{n}$ is

Integrals

Solution:

$S_{n}=\displaystyle\sum_{i=1}^{n} \frac{1}{n}\left(\frac{i}{n}\right)^{2014}$
$=\int\limits_{0}^{1} x^{2014} d x=\frac{1}{2015}$