New posts in Sequences And Series

Find $\lim_{n \to \infty}\frac{1}{2}+\frac{3}{2^2}+\frac{5}{2^3}+ \dots +\frac{2n-1}{2^n}$

Closed form of $\sum_{n=-\infty}^\infty \frac{(-1)^n}{\sinh (z+n)}$?

Does the order of the Fibonacci sequence's initial values matter?

$ \sum_{n=1}^{\infty} \frac{f(n)}{n^2} < +\infty$

Comparison test for $\sum_{n=1}^{\infty} \frac{\sqrt{n^5 + n^3 - n}}{2n^3 + 3n^2 + 1}$

Show that the sequence defined as $x_{n+1}=\sqrt[3]{x_n+x_{n-1}}$ converges

Why does this Infinite Series have contradictory convergences?

Showing $\sum_{k=1}^{n}k(k+1)(k+2)\cdots(k+r) = \frac{n(n+1)(n+2)\cdots(n+r+1)}{r+2}$

Find the sum: $\sum_{n=0}^\infty \frac{(n!)^2}{(2n)!}x^n$

Compute the limit of the sequence $x_n=(2-\sqrt{2})(2-\sqrt[3]{2})...(2-\sqrt[n]{2})$