New posts in summation

Prove using the method of double counting: $3^n =\sum_{k=0}^n \dbinom{n}{k} \sum_{j=0}^k \dbinom{k}{j}$ [duplicate]

combinatorics discrete-mathematics summation binomial-coefficients

Is there a closed-form of $\frac{\zeta (2)}{\pi ^2}+\frac{\zeta (4)}{\pi ^4}+\frac{\zeta (6)}{\pi ^6}+.....$

sequences-and-series summation zeta-functions

$\sum_{n=-\infty}^\infty e^{-\alpha n^2+\beta n}$

calculus real-analysis integration complex-analysis summation

Summation inductional proof: $\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\ldots+\frac{1}{n^2}<2$ [duplicate]

inequality summation induction

Relation between $\gcd$ and Euler's totient function .

elementary-number-theory summation gcd-and-lcm totient-function

Finding $\sum \frac{1}{n^2+7n+9}$

calculus summation

Can we assign a value to the sum of the reciprocals of the natural numbers?

sequences-and-series summation divergent-series

Is there a metric in which 1+2+3+4+... converges to -1/12?

metric-spaces summation riemann-zeta divergent-series regularization

Double summation, index change clarification.

discrete-mathematics summation

Proving that $1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\cdots+\frac{1}{2n-1}-\frac{1}{2n}=\frac{1}{n+1}+\frac{1}{n+2}+\cdots+\frac{1}{2n}$

sequences-and-series summation induction

Formula for finite power series

summation power-series geometric-series

Arithmetic pattern $1 + 2 = 3$, $4 + 5 + 6 = 7 + 8$, and so on

summation arithmetic

How to prove the sum of combination is equal to $2^n - 1$

sequences-and-series summation combinations exponentiation factorial

Fractional part summation

number-theory summation fractional-part

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

integration definite-integrals summation geometric-series

Computig the series $\sum\limits_{n=2}^\infty \ln\left(1-\frac{1}{n^2}\right)$

calculus real-analysis sequences-and-series summation

Using the rules that prove the sum of all natural numbers is $-\frac{1}{12}$, how can you prove that the harmonic series diverges?

convergence-divergence summation riemann-zeta

How would I express the series $|1+1+1|+|1+1-1|+|1-1+1|+|1-1-1|+|-1+1+1|+|-1+1-1|+|-1-1+1|+|-1-1-1|$ in summation notation?

summation notation

Has anyone heard of this maths formula and where can I find the proof to check my proof is correct? $\sum^n_{i = 1}i + \sum^{n-1}_{i=1}i = n^2$

proof-verification summation square-numbers

Find the sum $\frac{1}{\sqrt{1}+\sqrt{2}} + \frac{1}{\sqrt{2}+\sqrt{3}} + ...+ \frac{1}{\sqrt{99}+\sqrt{100}}$

algebra-precalculus summation radicals telescopic-series