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Need to prove the sequence $a_n=1+\frac{1}{2^2}+\frac{1}{3^2}+\cdots+\frac{1}{n^2}$ converges

real-analysis sequences-and-series convergence asked Mar 18 '13 at 2:56

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Functional Equation $f(x+y)=f(x)+f(y)+f(x)f(y)$

functional-equations asked Apr 21 '13 at 18:09

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I need to find all functions $f:\mathbb R \rightarrow \mathbb R$ which are continuous and satisfy $f(x+y)=f(x)+f(y)$

real-analysis functional-equations asked Apr 10 '13 at 2:40

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Need to prove $f$ continuous at $x_0$ iff for every monotonic sequence $(x_n)$ converging to $x_0$ we have $\lim f(x_n)=f(x_0)$

real-analysis limits convergence continuity cauchy-sequence asked Apr 10 '13 at 15:52

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Calculating Standard Gibbs Energy of Dissolution

physical-chemistry aqueous-solution solubility asked Dec 18 '13 at 6:47

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How can I tell if the sequence $a_n=\frac {2^n} {n!}$ converges, and if it converges what is its limit?

sequences-and-series limits asked Mar 15 '13 at 1:45

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Intermediate Value Property and Discontinuous Functions

real-analysis functions asked May 7 '13 at 5:57

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Need to prove the sequence $a_n=(1+\frac{1}{n})^n$ converges by proving it is a Cauchy sequence

homework real-analysis convergence asked Mar 19 '13 at 2:06

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How do I find the limit of the sequence $a_n=\frac{n\cos(n)}{n^2+1}$ and prove it is a Cauchy sequence?

real-analysis sequences-and-series limits cauchy-sequence asked Mar 16 '13 at 17:22

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