### Questions (30)

 11 Showing there's no closed-form: $\sum_{n=0}^\infty(-1)^n\frac{\cos^2({3^nx})}{3^n}$ 11 Prove that $\lim_{t \to \infty} \int_1^t \sin(x)\sin(x^2)\,dx$ converges 6 Evaluate $\sum_{n=1}^\infty \frac{1}{n}\frac{\ln{n}}{n-\ln{n}}$ [duplicate] 4 If $f'' \ge 0$, $\int_0^2 f(x)dx \ge 2f(1)$ 4 Find the function $f(x)$ if $f(x+y)=f(x-y)+2f(y)+xy$

### Reputation (765)

 +10 Solving the sequence $a_{n+1}=a_{n}a_{n-1}+\sqrt{(a_n^2-1)(a_{n-1}^2-1)}$: proving that $2+2a_n$ is a perfect square +110 Showing there's no closed-form: $\sum_{n=0}^\infty(-1)^n\frac{\cos^2({3^nx})}{3^n}$ +25 Prove that circumcircle of both triangles are equal +10 $a_{n+1}=a_{n}^2-2$, evaluate $\sum_{n=1}^\infty\frac{1}{a_1a_2\cdots a_n}$

 2 Combination Problem on white table 1 Prove that circumcircle of both triangles are equal

### Tags (42)

 2 probability 0 sequences-and-series × 15 2 combinations 0 limits × 8 1 triangles 0 trigonometry × 4 1 geometry 0 integration × 3 0 calculus × 29 0 convergence-divergence × 3

### Account (1)

 Mathematics 765 rep 1212 bronze badges