According to the Limit Comparison Test, when

an $>0$ and bn $>0,$

and

lim$$n$$$$

anbn

$=$ L$,$

where L is finite and positive, then the two series

an

$$and$$

bn

either both converge or both diverge.

We will compare the given series to

$15$n

$,$n $=1$

which converges as it is a geometric series with $|$r$|<1.$

Let

an $=$

$25$n $+1$

and

bn $=$

$15$

n$$

$.$

Substitute the values of

an and bn$,$

apply the limit

n$$$,$

and simplify it$.$

lim$$n$$$$

anbn

$=$lim$$n$$$$

$25$n $+1$

$1$ n

$=$lim$$n$$$$

$25$n n $+1$

$=$