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alukav5142 [94]
3 years ago
12

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

Mathematics
1 answer:
olya-2409 [2.1K]3 years ago
4 0

The terms in the sum are given by the sequence

\left\{\dfrac{5^{n+1}}{3^n}\right\}_{n\ge1}

We have

\dfrac{5^{n+1}}{3^n}>\dfrac{5^n}{3^n}=\left(\dfrac53\right)^n>1

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

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