Ononot — The Dirichlet eta function is defined as \eta(s) = \sum{n=1}

Guest Session: 1 Question Remaining. Create Account to save progress.

Power Serieshard

0:00.0

The Dirichlet eta function is defined as $\eta(s) = \sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n^s}$ for $s > 0$ . Consider the power series $f(x) = \sum_{n=1}^{\infty} \frac{(-1)^{n-1} x^n}{n^2}$ for $|x| \leq 1$ . What is $f(1)$ ?