Any P and C questions?

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Discussion Response Post to: Any P and C questions?

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®µD®A (2710)

Blazing goIITian

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@NugoRama dunno if it is correct ... i posted the same reply and someone told me that it was incorrect few months ago.

so better this way..

$\Gamma\ n=(n-1)!$

For n=1

$\Gamma\ 1=0!\\\Rightarrow 0!=1$

For those who want to know $\Gamma\ 1=1$

$\Gamma\ n=\int_0^{\infty}e^{-x}x^{n-1}dx$

$\Gamma\ 1=\int_0^{\infty}e^{-x}x^{1-1}dx\\\\=\lim_{b\to\infty}\int_0^{b}e^{-x}\\\\=\lim_{b\to\infty}[-e^{-x}]_0^b\\\\=\lim_{b\to\infty}(-e^{-b}+e^0)=0+1=1$

[IMG]http://alt1.artofproblemsolving.com/Forum/latexrender/pictures/0/6/3/0638cc54ee34d87aa803d78fe3ec072aa8749bf5.gif[/IMG] :)

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