limit question on a limit comparison test problem.

I understand why the limit comparison test is being used on this problem, but im not sure how they are simplifying B sub n into A sub n. i would of thought it would simplify to ((1+2^n)*(3^n))/((1+3^n)(2^n). Thanks.

problem.
http://i36.tinypic.com/24diqkk.jpg

solution.
http://i38.tinypic.com/14ocabo.jpg

Quote:

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Originally Posted by Evan.Kimia

I would of thought it would simplify to ((1+2^n)*(3^n))/((1+3^n)(2^n)

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Correct.
Take 2^n as common factor in the numerator, and 3^n as a common factor in the denominator. Cancel the same guys, and you will be fine.

There is another solution using the Basic Comparison Test:



and the last one is a convergent geometric series.