Very Very hard INTEGRATION

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samiul_samin
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Very Very hard INTEGRATION

Unread post by samiul_samin » Wed Feb 21, 2018 6:27 pm

Define $C(\alpha)$ to be the coefficient of $x^{1992}$ in the power series about $x=0$ of $(1+x)^{\alpha}$.Evaluate


$\int^1_0$ ($C$($-y-1$)$\sum_{k=1}^{1992} \dfrac {1}{y+k} $ )$dy$

Problem Source
Putnam $1994$

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samiul_samin
Posts: 1004
Joined: Sat Dec 09, 2017 1:32 pm

Re: Very Very hard INTEGRATION

Unread post by samiul_samin » Mon Feb 11, 2019 9:50 am

samiul_samin wrote:
Wed Feb 21, 2018 6:27 pm
Define $C(\alpha)$ to be the coefficient of $x^{1992}$ in the power series about $x=0$ of $(1+x)^{\alpha}$.Evaluate


$\int^1_0$ ($C$($-y-1$)$\sum_{k=1}^{1992} \dfrac {1}{y+k} $ )$dy$

Problem Source
Putnam $1994$
Hint
Use Taylor Series
Answer
$\fbox{1992}$
Solution This is problem from Putnum 1992 P2 .It is actually a trival prolem.

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