Find the $n^{th}$ term and sum to $n$ terms of the following series. $$1.3+2.4+3.5+……$$
My Attempt:
Here, $n^{th}$ term of $1+2+3+……=n$
$n^{th}$ term of $3+4+5+……=n+2$
Thus,
$n^{th}$ term of the series $1.3+2.4+3.5+……=n(n+2)$
$$t_n=n^2+2n$$
If $S_n$ be the sum to $n$ terms of the series then $$S_n=\sum t_n$$ $$=\sum (n^2+2n)$$
How do I proceed?