## Con..Con..confusion

For students of class 9-10 (age 14-16)
sakibtanvir
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### Con..Con..confusion

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)\$.
An amount of certain opposition is a great help to a man.Kites rise against,not with,the wind.

*Mahi*
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### Re: Con..Con..confusion

\$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.