The seriesdoes not converge.
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Examples 4.1.5(a): |
The series |
S n = -1 + 1 - 1 + 1 ... - 1 = -1if n is odd, and
S n = -1 + 1 - 1 + 1 ... - 1 + 1 = 0if n is even.
S n = -1 if n is odd and 0 if n is evenor, in other words, the sequence of partial sums is the same as the sequence
{ (-1) n }This sequence diverges, as proved before. Hence, our sequence of partial sums - while bounded - does not converge and therefore the series is divergent.