High Summation!

Calculus Level 5

0.051000r=0(1000+r)(1000+r1000)0.95r= ?0.05^{1000} \sum_{r=0}^{\infty} (1000+r){{1000+r}\choose{1000}}0.95^r = \ ?

(mn)=m!n!(mn)!\dbinom mn = \dfrac {m!}{n!(m-n)!} denotes the binomial coefficient.


All of my problems are original.

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