Sigma Notation Examples

Write the sum

using summation notation.

The nth term is

We want to start at n = 0, and keep going forever and ever...and ever. Instead, we write

Use summation notation to write the series

5(0.3)⁵ + 5(0.3)⁶ + 5(0.3)⁷ + ....

We could say the series starts at n = 5, since that's the exponent of the first term:

5(0.3)⁵ + 5(0.3)⁶ + 5(0.3)⁷ + ....

Then we would write the series as

Alternatively, we could decide we wanted to write the series starting at n = 0. In this case we'd think of the general term as

5(0.3)⁵(0.3)ⁿ.

Then we would write the series as