### Questions (14)

 4 Let $a_n$ be a decreasing sequence. Prove that the power series $\sum a_n x^n$ has no roots in $A=\{z\in C:|z|<1\}$ 2 Problem with holomorphic function and series 1 Prove that $\sum_{0\leq k\leq r} \binom{n+k}{k} \binom{m+n+k}{n+k} = \binom{m+n}{n} \binom{m+n+r+1}{m+n+1}$ where $m,n,r\in \mathbb{N}$ 1 $\int\limits_{S(1,1)} (\frac{z}{z-1} )^n dz$ 1 Is this definition referring to continuous or uniformly continuous function?

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 2 Gap series $\sum_{n=o}^\infty z^{n!}$ 1 Surround multiple close packed circles with a circle by general method. 1 How to calculate 0.5 million into thousands? 0 $T=\{\{x\}:x \in X\}$ Find $σ(Τ)$ where $X$ is a set and $σ(Τ)$ is the intersection of all σ-Algebras containing $T$ 0 How can I compare randomness with flipping and spinning a coin?

### Tags (25)

 2 complex-analysis × 14 0 measure-theory × 3 2 sequences-and-series × 3 0 analytic-functions × 2 1 geometry × 2 0 calculus × 2 1 analytic-geometry 0 statistics × 2 1 arithmetic 0 holomorphic-functions × 2

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 Mathematics 195 rep 1010 bronze badges