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bio website location India age 23 member for 1 year, 6 months seen 6 hours ago profile views 792

I am always an avid lover of Mathematics. I am now a graduate student on Telecommunication engineering. I have just started learning Real Analysis and Basic topology. Want to know the subjects more deeply and thoroughly. Currently following the book Mathematical analysis by Apostol and Introduction to Topology and modern analysis by Simmons.

These daunting busy days are keeping me from coming to this site. But I will return.

 14 How to find the sum of this series : $1+\frac{1}{2}+ \frac{1}{3}+\frac{1}{4}+\dots+\frac{1}{n}$ 13 Prove that $n < 2^{n}$ for all natural numbers $n$. 13 Prove that $z_{n+1} = \frac12 \left(z_n +\frac{1}{z_n} \right)$ converges to $1$ 10 $\lim_{x \to 1} \frac{x + x^2 + \dots + x^n - n}{x - 1} = \frac{n(n + 1)}{2}$ 8 How to find $\int_{0}^{1}\dfrac{\ln^2{x}\ln^2{(1-x)}}{2-x}dx$

# 5,860 Reputation

 +15 Find sum of quartic function coefficients by its plot +15 Finding ellips equation by focuses and tangent line +35 Show that $\left| \mathbb{P}(X=m)-\mathbb{P}(Y=m) \right| \le \mathbb{P}(Y\ne X)$ +10 Convergence of summable sequences

# 45 Questions

 9 Prime Mean of Primes 7 Evaluating $\int_0^L\int_0^L \cos^{-1}\left(\frac{x^2+y^2-a^2}{2xy}\right)xy~dx~dy$ 6 Nested Radical of Ramanujan 4 Primes in binary 3 Prime factorization of $10^n+1$

# 139 Tags

 90 calculus × 47 29 linear-algebra × 18 66 integration × 38 26 inequality × 9 58 sequences-and-series × 40 24 analysis × 11 37 real-analysis × 27 23 algebra-precalculus × 12 30 limits × 13 23 complex-analysis × 12

# 4 Accounts

 Mathematics 5,860 rep 624 Physics 101 rep 3 Signal Processing 101 rep 1 MathOverflow 101 rep 2