Con..Con..confusion

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sakibtanvir
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Con..Con..confusion

Unread post by sakibtanvir » Thu Feb 28, 2013 10:01 pm

I have a confusion in understanding a problem from Brilliant.org.Here is the problem and I request others not to give the solution nor the answer of the problem.I posted the problem to understand how the problem is operated!
A sequence of polynomials $f_{k}(x)$ is defined as follows
$f_{0}(x)=1$ ;$f_{k+1}(x)=f_{k}(x+1)+x^{k+1}$ , $k=0,1,2,3...$
Find the last three digits of the coefficient of $x$ in $f_{10}(x)$.
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*Mahi*
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Re: Con..Con..confusion

Unread post by *Mahi* » Thu Feb 28, 2013 10:55 pm

$f_0(x)=1$
$f_1(x) = f_0(x+1)+ x^1= 1+x$
$f_2(x) = f_1(x+1) + x^2 = (1+(x+1)) + x^2$
and so on, now the question says to find the last 3 digits of the coefficient of $x$ in $f_{10}(x)$.
And also, I really appreciate your honesty :) thanks.
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