Question

How do you use the comparison test (or the limit comparison test) for `(1+sin(x))/10^x`?

Answer 1

For the series `sum_(i=1)^oo (1+sin(n))/10^n` use `1+sinn <= 2`.

Explanation:

So `(1+sin(n))/10^n <= 2/10^n`

`sum_(i=1)^oo 2/10^n` is a geometric series with `r = 1/10` so it converges.