helios321

### Questions (114)

 7 For complex numbers $a,b,c$, explain why $a^{b\cdot c}=(a^b)^c$ is not necessarily true. 5 Evaluate: $\frac{1}{(1+1)!} + \frac{2}{(2+1)!}+…+\frac{n}{(n+1)!}$ using combinatorics. 5 Eigenvalues without any calculations 4 What is the geometric significance of differentiable vs continuously differentiable? 4 Proof of Fundamental Theorem of Calculus using big O

### Reputation (1,263)

 +20 If $A=\left\{a_{1}, a_{2}, \ldots, a_{p}\right\}$ is complete system of residue then $\sum_{1\leq i < j \leq p}a_ia_j \equiv 0 (\text{mod p})$. +10 Existence of $n \in \mathbb{Z}^+$ such that $b^{3^{n}}+b^{-3^{n}} \equiv 5 \,(\bmod~p\,)$ -2 For what values $\alpha>0$ does $\sum_{k\geq 1}\frac{k^{-\alpha}}{1+\alpha^{-k}}$ converge? +10 Spivak Chapter 11 Question 39

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### Tags (41)

 0 real-analysis × 62 0 uniform-convergence × 4 0 calculus × 19 0 taylor-expansion × 3 0 linear-algebra × 16 0 ordinary-differential-equations × 3 0 multivariable-calculus × 14 0 combinatorics × 3 0 sequences-and-series × 10 0 complex-analysis × 3

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 27 Changing a number between arbitrary bases

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