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**How to evaluate the definite integral!?**

## Homework Statement

Integral test to see if the series converges or diverges.

(infinity)

Sigma ((n^2)/(e^(n/3))

(n=1)

## Homework Equations

First I derive to make sure the function is decreasing and positive so it fits the criteria of the integral test.

It decreases when. 7=< x.

## The Attempt at a Solution

So I integrate it (using Integration by parts) and get to the point where I have to evaluate the definite integral

[(-3e^(-x/3))*(x^2+6x+18)] from 7 to a lim a-->infinity

This is where I get confused. My textbook says in sigma evaluate from 1 but in the answer it says plug in 7. I was wondering why this was?

My biggest problem is that If I plug these numbers in I have no idea how to simplify it down to a finite number. The answer is apparently 54 but I have no idea how to get there from here.