New posts in geometric-series

Manipulation of inferior and superior limits of a summation

summation geometric-series

Polynomial inequality: show $p(x) = \sum_{n=0}^{2k} x^n - \frac{1}{2k+1} \sum_{n=0}^{2k} (-x)^n\ge 0$

inequality polynomials optimization geometric-series

A Series with an increment in its difference .

sequences-and-series algebra-precalculus arithmetic-progressions geometric-series

Write $\frac {1}{1+z^2}$ as a power series centered at $z_0=1$

sequences-and-series power-series geometric-series

Summation problem.

calculus summation geometric-series

Finding the sum of geometric progression

summation geometric-series summation-method

Formula for finite power series

summation power-series geometric-series

A tough integral $\int_0^{\infty}\frac{\operatorname{sech}(\pi x)}{1+4x^2}\, \mathrm dx $

integration definite-integrals summation geometric-series

Is $1111111111111111111111111111111111111111111111111111111$ ($55$ $1$'s) a composite number?

sequences-and-series algebra-precalculus geometric-series geometric-progressions repunit-numbers

Double induction example: $ 1 + q + q^2 + q^3 + \cdots + q^{n-1} + q^n = \frac {q^{n+1}-1}{q-1} $

elementary-number-theory summation induction geometric-series

Induction (Geometric sequence)

sequences-and-series recurrence-relations geometric-series

Evaluating $\sum_{n=1}^\infty\frac{1}{2^{2n-1}}$

summation geometric-series

Crazy Iterated Square Roots

sequences-and-series radicals function-and-relation-composition nested-radicals geometric-series

What is wrong with the sum of these two series?

sequences-and-series paradoxes geometric-series

Evaluate $\lim\limits_{n\rightarrow \infty}\frac{n+n^2+n^3+\cdots +n^n}{1^n+2^n+3^n+\cdots +n^n}.$

calculus real-analysis sequences-and-series limits geometric-series

How to integrate $\int_0^{\infty} \frac{x}{e^x+1} dx$

integration definite-integrals riemann-zeta geometric-series

How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$?

sequences-and-series convergence-divergence power-series geometric-series faq