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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

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up vote 2 down vote accepted

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.

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and just times that by 4.945? – Gᴇᴏᴍᴇᴛᴇʀ Sep 26 '12 at 0:27
Yes, that's all that need to be done. – André Nicolas Sep 26 '12 at 0:29

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