Alternating Series Examples

Write the series

in expanded form.

This is a short series, so we can write all the terms. We plug each value of n into the general term a_n = n²:

We stick these terms together with plus signs, and we're done.

Write the series

in expanded form.

This series has 99 terms, so it's unreasonable to write down all of them. Find the first 3 terms and the last 2.

We write down these terms, stuck together with alternating plus and minus signs, and put dots in the middle for the terms we didn't compute:

Write the series

in expanded form.

We compute the first 3 terms, then write dots to show the pattern continues: