New posts in Sequence Of Function

Show that $\phi(x):=\sum_{n=1}^{\infty}\frac{(-1)^{n}}{\sqrt{n}(1+\frac{x^{2}}{n})^{n}}$ is differentiable on $\mathbb{R}$.

Show that the sequence of functions $\{f_n\}$ is not uniformly convergent on $\Bbb R.$

Proof that sequence converges to staircase function

Integral of sequence of functions

Evaluate the limit $\lim\limits_{n\to0}\frac{(x)+(2x)+\cdots (nx)}{n^2}$

Divergence of a sequence.

Summation problem: $f(x)=1+\sum_{n=1}^{\infty}\frac{x^n}{n}$

Finding the limit of a sequence of integrals

Uniform Convergence of $(\sin x)^n$