New posts in harmonic-numbers

Closed form for $\sum^\infty_{n=1}\frac{H_n}{2^n\,(2n+1)^2}$

calculus sequences-and-series closed-form harmonic-numbers polylogarithm

An identity satisfied by 'harmonic numbers' [duplicate]

summation intuition alternative-proof harmonic-numbers

Prove A New Method For Finding Primes.

harmonic-numbers

prove $\frac{1}{ n+1}+\frac{1}{ n+2}+\cdots+\frac{1}{2n}<\frac{25}{36}$ by mathematical induction

inequality induction harmonic-numbers

Find three integers in Harmonic Progression

sequences-and-series elementary-number-theory harmonic-numbers integer-sequences

Integral $\int^1_0\frac{\ln{x} \ \mathrm{Li}_2(x)}{1-x}dx$

integration definite-integrals summation harmonic-numbers polylogarithm

Proving $\sum_{k=1}^{n}{(-1)^{k+1} {{n}\choose{k}}\frac{1}{k}=H_n}$

summation binomial-coefficients inclusion-exclusion harmonic-numbers coupon-collector

Harmonic Numbers series I

sequences-and-series generating-functions closed-form catalan-numbers harmonic-numbers

Proof by induction of summation inequality: $1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\dots+\frac1{2^n}\ge 1+\frac{n}2$

inequality summation induction harmonic-numbers

Closed form of Euler-type sum over zeta functions $\sum _{k=2}^{\infty } \frac{\zeta (k)}{k^2}$?

summation riemann-zeta harmonic-numbers euler-mascheroni-constant

How to show that $\lim \frac{1}{n} \sum_{i=1}^n \frac{1}{i}=0 $? [duplicate]

sequences-and-series limits convergence-divergence harmonic-numbers

Evaluating the challenging sum $\sum _{k=1}^{\infty }\frac{H_{2k}}{k^3\:4^k}\binom{2k}{k}$.

real-analysis integration sequences-and-series definite-integrals harmonic-numbers

Mathematical induction for inequalities: $\frac1{n+1} + \frac1{n+2} + \cdots +\frac1{3n+1} > 1$

inequality summation induction harmonic-numbers

On twisted Euler sums

sequences-and-series residue-calculus riemann-zeta harmonic-numbers summation-by-parts

Why is there no general form for the harmonic numbers?

elementary-number-theory closed-form harmonic-numbers

Double Euler sum $ \sum_{k\geq 1} \frac{H_k^{(2)} H_k}{k^3} $

real-analysis sequences-and-series complex-analysis harmonic-numbers polylogarithm

A proof of $\sum_{i=1}^{n}(-1)^{i-1}\binom{n}{i}\frac{1}{i}=\frac{1}{1}+\frac{1}{2}+....+\frac{1}{n}$ [duplicate]

integration sequences-and-series definite-integrals harmonic-numbers

Are we guaranteed that the harmonic series minus infinite random terms always converge?

sequences-and-series random-variables harmonic-numbers

Prove that $1<\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{3n+1}$

inequality summation induction harmonic-numbers

Showing that $\sum_{i=1}^n \frac{1}{i} \geq \log{n}$

calculus inequality summation harmonic-numbers