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# recursive sequence

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Let $a_n$ be a recursive function satisfying $a_n=a_{n-1}+2n-1$ for all positive integers $n$, and $a_0=0$. What is the value of $\displaystyle \sum _{n=1}^{100}a_n$?

Feb 4, 2021

Notice that $a_n=n^2$. By the sum of squares formula, the answer is $\frac{100(100+1)(2*100+1)}{6}=\boxed{338350}$.