## Comparison Test

### Examples 4.2.4(a):

Because *| sin(x) | 1*
for all real number *x*, we have that

But is a special case of the geometric series, which converges. Hence, by the comparison test, the original series converges absolutely.1 / 2^{n}sin(n) | | 1 / 2^{n}|

Note that, formally, we could say: Since

for all| 1 / 2^{n}sin(n) | | 1 / 2^{n}|

*n*. We also have

"Therefore", the series converges absolutely.| | <