# 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 geometric problem solved with Pigeon Hole Principle 11 Surprising identities / equations 10 How to efficiently compute $17^{23} (\mod 31)$ by hand? 10 Can't simplify this fraction: $\frac{1+x^6}{1+x^2}$

# 4,467 Reputation

 +10 which is larger number? $\sqrt{7}-\sqrt{6}$ or $\sqrt{6}-\sqrt{5}$ +10 Prove that $\tan A + \tan B + \tan C = \tan A\tan B\tan C,$ $A+B+C = 180^\circ$ +10 Obtain polar form of a line from two points +15 Number puzzle from NAPLAN practice quiz, I know the answer, but I can't figure out why it is the answer

# 25 Questions

 32 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?

# 87 Tags

 65 algebra-precalculus × 26 20 elementary-number-theory × 9 42 homework × 21 20 linear-algebra × 8 31 number-theory × 14 19 calculus × 11 22 combinatorics × 5 18 polynomials × 8 20 trigonometry × 15 17 fractions × 4

# 14 Accounts

 Mathematics 4,467 rep 11136 Meta Stack Exchange 123 rep 3 Stack Overflow 106 rep 3 Area 51 106 rep 2 Server Fault 101 rep