Finding sum of none arithmetic series I have a question to find the sum of the following sum:
$$
S = \small{1*1+2*3+3*5+4*7+...+100*199}
$$
I figured out that for each element in this series the following holds:
$$
a_n = a_{n-1} + 4n - 3
$$
But I don't know where to go from here, I tried subtracting some other series but that did not work very well

This is, for $n=100$,
$s(n)
=\sum_{k=1}^n k(2k-1)
=\sum_{k=1}^n (2k^2-k)
=2\sum_{k=1}^n k^2
-\sum_{k=1}^n k
$.
Plug in the formulas for the sums
and you are done.
