jon jones
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### Questions (22)

 14 Prove that $\left (\frac{a^2 + b^2 +c^2}{a+b+c} \right) ^ {(a+b+c)} > a^a b^b c^c$ 11 $\epsilon{\rm -}\delta$ proof of the discontinuity of Dirichlet's function 8 How to show that that $\sum_{n=1}^{\infty}\left( \frac{1}{3n-1} + \frac{1}{3n-2}- \frac{2}{3n}\right)= \ln\left(3\right)$? 7 Composite number 6 Derivative of $x^x$ at $x=1$ from first principles

### Reputation (581)

 +5 Harmonic Series. +5 Sequence Limit: $\lim\limits_{n \rightarrow \infty}{n\,x^n}$ +5 Derivative of $x^x$ at $x=1$ from first principles +5 How to show that that $\sum_{n=1}^{\infty}\left( \frac{1}{3n-1} + \frac{1}{3n-2}- \frac{2}{3n}\right)= \ln\left(3\right)$?

 5 Use the ε-δ definition of a limit to prove this. 4 Proving that $\lim\limits_{x \to 0}\frac{e^x-1}{x} = 1$ 1 Prove that if $n$ is a positive integer then $2^{3n}-1$ is divisible by $7$.

### Tags (16)

 9 limits × 9 1 divisibility 5 calculus × 7 0 sequences-and-series × 6 4 derivatives × 2 0 linear-algebra × 2 4 exponential-function 0 multivariable-calculus × 2 1 elementary-number-theory × 4 0 natural-numbers × 2

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