induction with recursive elements $y_{k}=y_{k-1}+k^2$ the problem is $y_{k}=y_{k-1}+k^2$, for all integers k $>=$ 2 given $y_{1}=1$ Honestly I got caught up with this question $y_{2}=1+2^2 = 1+4 = 5$ $y_{k+1}=y_{k}+(k+1)^2$ -plugging in $y_{k}$ $y_{k+1}=y_{k-1}+k^2+(k+1)^2$ - foiling out $(k+1)^2$ $y_{k+1}=y_{k-1}+k^2+k^2+2k+1$ I have no clue where to go from here or if i'm even on the right track if anyone can give me some help it would be appreciated thank you

We have $y_{k}=y_{k-1}+k^2$, so \begin{eqnarray*} y_{k}=k^2+(k-1)^2+ \cdots+ 1 =\sum_{i=1}^{k} i^2 =\frac{n(n+1)(2n+1)}{6}. \end{eqnarray*}