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  1. Find out the generating function for $S_n = 1^2 + 2^2 + 3^2 + 4^2 + ... n^2$ and with that generating function show that it is equal to $\begin{align*} \frac{n\left ( n+1 \right )\left ( 2n+1 \right )}{6} \end{align*}$
  2.  Find out the generating function for $S_n = 1^3 + 2^3 + 3^3 + 4^3 + ... n^3$ and with that generating function show that it is equal to $\begin{align*} \left ( \frac{n\left ( n+1 \right )}{2} \right )^2 \end{align*}$
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