N'th Differencial

For discussing Olympiad Level Algebra (and Inequality) problems
Corei13
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N'th Differencial

Unread post by Corei13 » Tue Dec 21, 2010 10:56 pm

Prove that, for any function $f(x)$,

\[ \frac{{d^{n}}}{{dx^{n}}}f(x)=\lim_{h\to 0}\frac{\sum_{i=0}^{n}{(-1)^{i}}\binom{n}{i}f(x+(n-i)h)}{h^{n}} \]
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Moon
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Re: N'th Differencial

Unread post by Moon » Wed Dec 22, 2010 12:14 am

Is it your own problem? I'd like to request everyone to write a few words about the source of the problem. (You should hide the sources in some cases)
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.

Corei13
Posts: 153
Joined: Tue Dec 07, 2010 9:10 pm
Location: Chittagong

Re: N'th Differencial

Unread post by Corei13 » Wed Dec 22, 2010 1:03 am

অামার প্রবলেম বলতে নিজেই বের করসি, কিন্তু অাগেও নিশ্চয় কেউ বের করসে।
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zadid xcalibured
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Re: N'th Differencial

Unread post by zadid xcalibured » Thu Feb 28, 2013 2:27 am

Induction and combinatorial argument both yeilds easy solution. :mrgreen:

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