quartz
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 12 How I can prove that the sequence $\sqrt{2} , \sqrt{2\sqrt{2}}, \sqrt{2\sqrt{2\sqrt{2}}}$ converges to 2? 6 Find the maximum value of the product xyz? 6 Proving $\sum_{k=1}^n k\cdot k! = (n+1)!-1$ without using mathematical Induction. 5 Why everytime the final number comes the same? 4 Proving that a natural number is divisible by $3$

### Reputation (879)

 +30 How I can prove that the sequence $\sqrt{2} , \sqrt{2\sqrt{2}}, \sqrt{2\sqrt{2\sqrt{2}}}$ converges to 2? +10 Proving $\sum_{k=1}^n k\cdot k! = (n+1)!-1$ without using mathematical Induction. +10 How to prove $\lim_{n\rightarrow \infty} {a^n \over n!}=0$ +5 Cauchy Riemann equations for real functions.

### Questions (8)

 14 Why aren't all dense subsets of $\mathbb{R}$ uncountable? 6 what is value of $\lim_{n\to\infty} n^{-2}e^{(\log(n))^a}$? 5 What is the value of $\displaystyle\lim_{R\to\infty} {\int_R^{\infty}{r^ne^{-r^2/2}dr}\over{R^{n-1}e^{-R^2/2}}}$ 4 How to construct a dense subset of $\mathbb R$ other than rationals. 3 Is there is a number system which is extension of complex number system?

### Tags (24)

 21 sequences-and-series × 6 6 inequality 18 real-analysis × 8 5 puzzle 11 algebra-precalculus × 2 4 calculus × 3 6 alternative-proof 4 elementary-number-theory 6 factorial 3 limits × 3

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