# Shobhit

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 15 Prove that $1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+…+\frac{1}{199}-\frac{1}{200}=\frac{1}{101}+\frac{1}{102}+…+\frac{1}{200}.$ 12 Surprising identities / equations 12 geometric problem solved with Pigeon Hole Principle 10 How to efficiently compute $17^{23} (\mod 31)$ by hand? 10 Can't simplify this fraction: $\frac{1+x^6}{1+x^2}$

# 4,546 Reputation

 +3 Questions on the empty set $\varnothing$ +20 How can I prove that $a^n + b$ is composite? +5 Plotting a polar curve +5 How to prove $\sqrt{5+\sqrt{5+\sqrt{5-\sqrt{5+\sqrt{5+\sqrt{5+\sqrt{5-\cdots}}}}}}} = \frac{2+\sqrt 5 +\sqrt{15-6\sqrt 5}}{2}$

# 28 Questions

 34 How to prove $\sqrt{5+\sqrt{5+\sqrt{5-\sqrt{5+\sqrt{5+\sqrt{5+\sqrt{5-\cdots}}}}}}} = \frac{2+\sqrt 5 +\sqrt{15-6\sqrt 5}}{2}$ 23 The final number after $999$ operations. 7 The product of two natural numbers with their sum cannot be the third power of a natural number. 6 Find the sum of series $\sum_{n=0}^\infty\frac{(4n)!}{(4n+4)!}$ 6 tough algebric problem?

# 91 Tags

 65 algebra-precalculus × 26 20 linear-algebra × 8 31 number-theory × 14 19 calculus × 12 22 combinatorics × 5 18 polynomials × 8 20 trigonometry × 15 17 fractions × 4 20 elementary-number-theory × 9 15 irrational-numbers × 2

# 15 Accounts

 Mathematics 4,546 rep 11137 Meta Stack Exchange 128 rep 3 Stack Overflow 106 rep 3 Area 51 106 rep 2 Server Fault 101 rep