Summation of Polynomial Series
To evaluate any series of the formwe

Expand the brackets and express as a sum of different summation terms. In this case we obtain

Now use use the linearity properties of summation to obtain:

Now use standard formulae to express each term in terms of n.

Add the terms. Expand and simply the expression
Example Prove
1
2 There are no constants to take out.
3. Use the standard formulae.
.

Subtract the second and third from the first. Expand and simplify.