Writing infinite series

Here's how to write

1 - \frac{1}{2} - \frac{1}{4} + \frac{1}{3} - \frac{1}{6} - \frac{1}{8} + \frac{1}{5} - . . . .

using the

\sum

notation:

1 - \frac{1}{2} - \frac{1}{4} + \frac{1}{3} - \frac{1}{6} - \frac{1}{8} + \frac{1}{5} - . . . . = \sum_{i = 0}^{\infty} \frac{1}{2 i + 1} - \frac{1}{4 i + 2} - \frac{1}{4 i + 4} .