Summation of Polynomial Series

To evaluate any series of the formwe

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

2. Now use use the linearity properties of summation to obtain:

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

4. Add the terms. Expand and simply the expression

Example Prove

1

2 There are no constants to take out.

3. Use the standard formulae.

.

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