## 4.1. Series and Convergence

### Examples 4.1.5(a):

Consider the sequence of partial sums:ifS_{n}= -1 + 1 - 1 + 1 ... - 1 = -1

*n*is odd, and

ifS_{n}= -1 + 1 - 1 + 1 ... - 1 + 1 = 0

*n*is even.

or, in other words, the sequence of partial sums is the same as the sequenceSif_{n}= -1nis odd and 0 ifnis even

This sequence diverges, similar to the sequence{^{1}/_{2}((-1)^{n}-1)}

*{(-1)*we discussed previously. Hence, our sequence of partial sums - while bounded - does not converge and therefore the series is divergent.

^{n}}