grandes-ecoles 2019 Q16

grandes-ecoles · France · centrale-maths2__pc Sequences and Series Uniform or Pointwise Convergence of Function Series/Sequences

For every $s > 1$, let $\zeta(s) = \sum_{n=1}^{+\infty} \frac{1}{n^s}$. Show that $\zeta$ is continuous on $]1, +\infty[$.

For every $s > 1$, let $\zeta(s) = \sum_{n=1}^{+\infty} \frac{1}{n^s}$. Show that $\zeta$ is continuous on $]1, +\infty[$.