Question

Determine whether the series is convergent or divergent. If convergent, find the sum; if divergent, enter div . ∑n=1[infinity]3n(n+2)

Answer 1

The series ∑n=1[∞]3n(n+2) is divergent because as n approaches infinity, the terms do not tend toward zero, which is a necessary condition for convergence.

Step-by-step explanation:

The question asks to determine whether the series expansion ∑n=1[∞]3n(n+2) is convergent or divergent and to find the sum if it is convergent. To analyze the convergence, we can use the ratio test or comparison test, but it is immediately clear that this series diverges. The terms of the series do not approach zero as n approaches infinity because the numerator of each term grows without bound as the degree of the polynomial in the numerator is higher than that in the denominator. This violates the necessary condition for series convergence that the terms approach zero.

Answer 2

div

Step-by-step explanation:

`\sum\limits^\infty_(n=1){3n(n+2)} \rightarrow\infty`

The infinite sum of any polynomial terms will be divergent.