# Ramanujan

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 15 Prove that $1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+…+\frac{1}{199}-\frac{1}{200}=\frac{1}{101}+\frac{1}{102}+…+\frac{1}{200}.$ 13 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: $\frac{1+x^6}{1+x^2}$

# 4,565 Reputation

 +10 Fraction raised to integer power +10 Prove that $\tan A + \tan B + \tan C = \tan A\tan B\tan C,$ $A+B+C = 180^\circ$ +10 Probability on divisibility +5 How to prove $\sqrt{5+\sqrt{5+\sqrt{5-\sqrt{5+\sqrt{5+\sqrt{5+\sqrt{5-\cdots}}}}}}} = \frac{2+\sqrt 5 +\sqrt{15-6\sqrt 5}}{2}$

# 31 Questions

 35 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 tough algebric problem? 5 Find the sum of series $\sum_{n=0}^\infty\frac{(4n)!}{(4n+4)!}$

# 91 Tags

 66 algebra-precalculus × 28 19 calculus × 12 32 number-theory × 14 19 elementary-number-theory × 9 22 trigonometry × 15 18 polynomials × 8 22 combinatorics × 5 18 fractions × 5 20 linear-algebra × 8 16 irrational-numbers × 2

# 17 Accounts

 Mathematics 4,565 rep 11138 Meta Stack Exchange 128 rep 3 Mathematica 127 rep 4 Stack Overflow 106 rep 3 Area 51 106 rep 2