Name:
Anonymous
2008-11-03 13:35
is the infinite series (1/4 + (-1)^n)/n absolutely convergent?
Name:
Anonymous
2008-11-04 0:11
\sum_{n=1}^{\infty} \frac{\frac{1}{4} + (-1)^n}{n}
= \sum_{n=1}^{\infty} \left(\frac{1}{4n} + \frac{(-1)^n}{n} \right)
= \frak{1}{4}\sum_{n=1}^\infty \frak{1}{n} + \sum_{n=1}^\infty \frak{(-1)^n}{n}
= \infty + 2
= \infty
looks like this works