How to find sum of quadratic

Question

I got this quadratic function from physics that I need to find the sum of each term, up to whatever point. Written thusly:

$$ \sum_{n=1}^{t}4.945n^2$$

And is there someway to quickly figure this out? Or links to tutorials

Answer 1

There is the standard formula $$\sum_{k=1}^n k^2=\frac{n(n+1)(2n+1)}{6}.$$

It can be proved by a pretty routine induction.