The divergence of the reciprocals of odd integers

• October 28th 2009, 05:17 PM
paupsers
The divergence of the reciprocals of odd integers
Can anyone prove whether
S = 1 + 1/3 + 1/5 + ... + 1/(2n-1)
converges or diverges?
• October 28th 2009, 05:30 PM
redsoxfan325
Quote:

Originally Posted by paupsers
Can anyone prove whether
S = 1 + 1/3 + 1/5 + ... + 1/(2n-1)
converges or diverges?

$\sum_{n=1}^{\infty}\frac{1}{2n}\leq\sum_{n=1}^{\in fty}\frac{1}{2n-1}$

Use the comparison test.