# shaswata

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418
bio website proofwords.blogspot.com location India age 18 member for 1 year, 9 months seen Nov 30 at 18:27 profile views 214

12th grade student.Interested in maths,physics and any form of puzzle.

 47 Comparing $\sqrt{1001}+\sqrt{999}\ , \ 2\sqrt{1000}$ 10 Proving $\sum_{k=1}^n{k^2}=\frac{n(n+1)(2n+1)}{6}$ without induction 9 What is $\pi$ in mathematics; does $\pi = 3.14$? From where does it come? 9 Irrationality of $\sqrt 2$ using induction 8 Evaluating $\lim\limits_{n\to \infty}\left\{(1+\frac{1}{n})(1+\frac{2}{n})\dots(1+\frac{n}{n})\right\}^{\frac{1}{n}}$

# 2,821 Reputation

 +10 Unit diameter pentagons with maximum area +10 There always exists a sequence of consecutive composite integers of length $n$ for all $n$. +10 Comparing $\sqrt{1001}+\sqrt{999}\ , \ 2\sqrt{1000}$ +10 Show that $7\mid(3^{2n+1}+2^{n+2})$ for all $n\in\mathbb{N}$

# 14 Questions

 32 Finding the sum- $x+x^{2}+x^{4}+x^{8}+x^{16}\cdots$ 13 Polynomial $P(a)=b,P(b)=c,P(c)=a$ 11 $\cos(x)+\cos(x\sqrt{2})$ is not periodic 8 Last digits of a power of 2 7 Cross section is a regular hexagon.Is it a cube?

# 54 Tags

 60 algebra-precalculus × 6 16 summation × 3 47 problem-solving × 2 13 limits × 4 30 elementary-number-theory × 8 12 polynomials × 6 24 calculus × 11 11 sequences-and-series × 8 18 induction × 6 10 alternative-proof × 2

# 4 Accounts

 Mathematics 2,821 rep 418 Physics 111 rep 2 MathOverflow 111 rep 1 Chemistry 101 rep