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Question Number 28620 by abdo imad last updated on 28/Jan/18

$$calculate\sum _{n=p}^{+\mathrm{\infty }}{C}_n^p{x}^n.$$

Commented by Tinkutara last updated on 28/Jan/18

$$Howcann>pbecasuceitisusedin$$$${}^p{C}_n?$$

Commented by abdo imad last updated on 28/Jan/18

$$\sum _{n=p}^{\propto }{C}_n^p{x}^n=C_p^p{x}^p+C_{p+1}^p{x}^{p+1}+...$$

Commented by Tinkutara last updated on 28/Jan/18

$$Butwhatis{}^p{C}_{p+1}?Isitcombination?$$$$Becauseifwewrite{}^n{C}_{r}itmeans$$$$r⩽n.$$

Commented by abdo imad last updated on 28/Jan/18

$$forusweuse{C}_n^p=\frac{n!}{p!(n-p)!}forp⩽nitsonlyanotation$$$$ofcombination..$$

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