Question

(5CQ) Use the comparison test to determine whether the series 25/3+125/9+625/27+... is convergent or divergent.

Answer 1

B. Divergent

Explanation:

Did test

Answer 2

The terms in the sum are given by the sequence

`\left\{(5^(n+1))/(3^n)\right\}_(n\ge1)`

We have

`(5^(n+1))/(3^n)>(5^n)/(3^n)=\left(\frac53\right)^n>1`

for all
`n`, and the series
`1+1+1+\cdots` clearly diverges, so
`\frac{25}3+\frac{125}9+\cdots` must also diverge.