# Kirthi Raman

"You have enemies? Good. That means you've stood up for something, sometime in your life" - Winston Churchill

Top Questions

## Evaluating $\int_0^1 \log \log \left(\frac{1}{x}\right) \frac{dx}{1+x^2}$

asked Mar 18 '12 at 0:44

## Solve the integral $S_k = (-1)^k \int_0^1 (\log(\sin \pi x))^k dx$

asked Mar 17 '12 at 21:00

## Let $a,b$ be positive real numbers. Prove $\frac{1}{\sqrt{1+a^2}}+\frac{1}{\sqrt{1+b^2}} \geq \frac{2}{\sqrt{1+ab}}$

asked Mar 27 '12 at 2:10

## Let $n$ be a positive integer such that $\displaystyle{\frac{3+4+\cdots+3n}{5+6+\cdots+5n} = \frac{4}{11}}$

asked Mar 18 '12 at 1:40

## Prove for any positive real numbers $a,b,c$ $\frac{a^3}{a^2+ab+b^2}+\frac{b^3}{b^2+bc+c^2}+\frac{c^3}{c^2+ca+a^2} \geq \frac{a+b+c}{3}$

asked Mar 21 '12 at 1:04

## Prove $1^a+2^a+\cdots+n^a < \frac{(n+1)^{(a+1)}-1}{a+1}$ for any $a >0$ and $n \in \mathbb{Z^+}$

asked Mar 27 '12 at 1:36

## Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$

asked Mar 23 '12 at 12:18

## What is the largest positive $n$ for which $n^3+100$ is divisible by $n+10$

asked Mar 27 '12 at 2:15