40 How to find the sum of this series : $1+\frac{1}{2}+ \frac{1}{3}+\frac{1}{4}+\dots+\frac{1}{n}$ 18 Prove that $n < 2^{n}$ for all natural numbers $n$. 17 What functions satisfy such equation? 17 How to compute $\prod_{n=1}^\infty\left(1+\frac{1}{n!}\right)$? 17 How to show $\lim_{x \to 1} \frac{x + x^2 + \dots + x^n - n}{x - 1} = \frac{n(n + 1)}{2}$?

Reputation (14,191)

 +10 How to find the sum of this series : $1+\frac{1}{2}+ \frac{1}{3}+\frac{1}{4}+\dots+\frac{1}{n}$ +10 How do you express the Frobenius norm of a Matrix as the squared norm of its singular values? +10 Minimize $f(x,y,z)={(x-3)^2+y^2+z^2}$ using Lagrange Multipliers given the constrain $z=\frac{x^2}{4}+\frac{y^2}{25}$ +10 uniform random point in triangle

Questions (72)

 14 Are eigenvalues of the limit of a sequence of matrices limits of eigenvalue sequences? 11 Nested Radical of Ramanujan 10 Prime Mean of Primes 9 An inequality concerning restricted isometry property 8 Evaluating $\int_0^L\int_0^L \cos^{-1}\left(\frac{x^2+y^2-a^2}{2xy}\right)xy~dx~dy$

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 220 sequences-and-series × 89 78 limits × 31 213 calculus × 90 68 analysis × 25 137 integration × 63 64 summation × 14 115 real-analysis × 75 62 algebra-precalculus × 17 82 linear-algebra × 47 56 harmonic-numbers × 2

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