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### Questions (38)

 18 Induction: $\sum_{k=0}^n \binom nk k^2 = n(1+n)2^{n-2}$ 10 Prove that $(e+x)^{e-x}>(e-x)^{e+x}$ 8 Is $f(x)= \cos(e^x)$ uniformly continuous? 5 Prove $\sum_{i=1}^{n}\frac{x_{i}^3}{x_{i+1}^2}\geq \sum_{i=1}^{n}\frac{x_{i}^2}{x_{i+1}}$ 5 expand $\arctan\left(\frac{3x+2}{3x-2}\right)$ into pwer series, find radius of convergence (check solution)

### Reputation (708)

 +5 Induction: $\sum_{k=0}^n \binom nk k^2 = n(1+n)2^{n-2}$ +5 Prove $\sum_{i=1}^{n}\frac{x_{i}^3}{x_{i+1}^2}\geq \sum_{i=1}^{n}\frac{x_{i}^2}{x_{i+1}}$ +5 Prove that $(e+x)^{e-x}>(e-x)^{e+x}$ +5 Limit: $\lim_{n\rightarrow\infty} \sqrt[n]{{\frac{1}{\sqrt{3}}((\frac{1+\sqrt{3}}{2})^n}-(\frac{1-\sqrt{3}}{2})^n)}$

 2 Limit calculation using Riemann integral 0 Power Series Proof w/ Binomial Coef.

### Tags (17)

 2 analysis × 8 0 sequences-and-series × 5 2 integration × 3 0 power-series × 5 0 limits × 19 0 linear-algebra × 4 0 real-analysis × 16 0 induction × 3 0 calculus × 7 0 algebra-precalculus × 2

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