Question

Is the series (8+1^n)/(1+2^n) divergent or convergent?

Answer 1

your numerator is 9, the denominator gets bigger, so the result approaches zero

so it is convergent.

Answer 2

that doesn't mean it's convergent, necessarily.
but i found it is actually convergent because if you divide by 1/2^n, which is also a positive term series, you get 9, which means the series is convergent.