sachin

### Questions (332)

 33 How to find the sum of this series : $1+\frac{1}{2}+ \frac{1}{3}+\frac{1}{4}+\dots+\frac{1}{n}$ 17 Evaluate the limit $\lim\limits_{n \to \infty} \frac{1}{1+n^2} +\frac{2}{2+n^2}+ \ldots +\frac{n}{n+n^2}$ 14 Integrate : $\int \frac{x^2}{(x\cos x -\sin x)(x\sin x +\cos x)}dx$ 13 How to find the sum of this : $\sqrt{1+\frac{1}{1^2}+\frac{1}{2^2}}+ \sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}+\sqrt{1+\frac{1}{3^2}+\frac{1}{4^2}}+…$ 13 How to find the sum of the sequence $\frac{1}{1+1^2+1^4} +\frac{2}{1+2^2+2^4} +\frac{3}{1+3^2+3^4}+…$

### Reputation (4,358)

 +5 Find the sum : $\sin^{-1}\frac{1}{\sqrt{2}}+\sin^{-1}\frac{\sqrt{2}-1}{\sqrt{6}}+\sin^{-1}\frac{\sqrt{3}-\sqrt{2}}{\sqrt{12}}+\cdots$ +5 Given that $\;\sin^3x\sin3x = \sum^n_{m=0}C_m\cos mx\,,\; C_n \neq 0\;$ is an identity . Find the value of n. +5 complex numbers modulus problems +5 Probability : A bag contains 12 pair socks . Four socks are picked up at random. Find the probability that there is at least one pair.

 3 What is the proof that the total number of subsets of a set is $2^n$? 3 Need help in proving that $\frac{\sin\theta - \cos\theta + 1}{\sin\theta + \cos\theta - 1} = \frac 1{\sec\theta - \tan\theta}$ 3 Solving $x^{\log(x)}=\frac{x^3}{100}$ 2 Finding minimum $\frac{x+y}{z}+\frac{x+z}{y}+\frac{y+z}{x}$ 2 How does one derive these solutions to the cubic equation?

### Tags (63)

 6 trigonometry × 48 3 logarithms × 8 5 integration × 46 3 discrete-mathematics × 2 4 combinatorics × 6 3 elementary-set-theory 4 problem-solving × 2 2 calculus × 115 3 indefinite-integrals × 10 2 algebra-precalculus × 103