# sequence converge or diverge

• April 6th 2009, 10:19 PM
VkL
sequence converge or diverge
Does the sequence converge or diverge? If the sequence converges, to what value?

( (-0.1)^n ) / n

The Limit if this goes to zero, so it must converge i'm assuming. ??
• April 6th 2009, 11:25 PM
Reckoner
Quote:

Originally Posted by VkL
The Limit if this goes to zero, so it must converge i'm assuming. ??

If the limit is zero, then the sequence converges to zero. This is by definition.

And in this case we do have

$\lim_{n\to\infty}\frac{(-0.1)^n}n$

$=\lim_{n\to\infty}\frac{(-1/10)^n}n$

$=\lim_{n\to\infty}(-1)^n\frac{1/10^n}n$

$=\lim_{n\to\infty}(-1)^n\frac1{n10^n}$

$=0.$