### Answers (140)

 8 How to show that $\int_0^1\frac{\sin(\frac{1}{x})}{x^2}dx$ diverges? 8 Proving the convergence of the sequence defined by $x_1=3$ and $x_{n+1}=\frac{1}{4-x_n}$ 6 Evaluate $\int \frac{2-x^3}{(1+x^3)^{3/2}} dx$ 6 Help with the last step in solving $\lim_{x\to0}\frac{(1+\sin x +\sin^2 x)^{1/x}-(1+\sin x)^{1/x}}x$ 6 How to prove that $\sum_{k=0}^n{(-1)^k{4n-2k\choose 2n}{2n\choose k}}=2^{2n}$?

### Reputation (3,179)

 +10 The number of integral solution of $\alpha+\beta+\gamma+\delta$=18 such that.. +10 Lattice point problem +10 Find the area of the part of the surface $z=x^2+y^2+2$ that lies above the disc $x^2+y^2 \le 1$ +10 How do I evaluate $\lim_{n\to\infty} \,\sum_{k=1}^n\left(\frac{k}{n^2}\right)^{\frac{k}{n^2}+1}$?

### Tags (127)

 45 calculus × 21 20 trigonometry × 13 32 real-analysis × 12 20 combinatorics × 10 25 sequences-and-series × 10 15 algebra-precalculus × 15 21 integration × 13 15 limits × 7 21 multivariable-calculus × 10 15 summation × 6

### Bookmarks (71)

 800 The staircase paradox, or why $\pi\ne4$ 242 Evaluating $\lim\limits_{n\to\infty} e^{-n} \sum\limits_{k=0}^{n} \frac{n^k}{k!}$ 216 How can a piece of A4 paper be folded in exactly three equal parts? 120 All real numbers in $[0,2]$ can be represented as $\sqrt{2 \pm \sqrt{2 \pm \sqrt{2 \pm \dots}}}$ 96 Why is the volume of a cone one third of the volume of a cylinder?

### Accounts (28)

 Mathematics 3,179 rep 44 silver badges1212 bronze badges Physics 500 rep 22 silver badges99 bronze badges Stack Overflow 101 rep 22 bronze badges Electrical Engineering 101 rep 11 bronze badge Code Golf 101 rep 11 bronze badge

### Badges (15)

 Constituent Yearling × 2 Mortarboard Informed Caucus Commentator Cleanup Critic Enthusiast Explainer

### Active bounties (0)

This user has no active bounties

### Votes cast (246)

all time   by type
199 up 102 question
47 down 144 answer