Find the limit of the sequence or why it diverges?

a_n = (2*3^n+9*5^n)/(10*3^n+21*5^n)

1 Answer
Jul 20, 2017

I solved it within minutes of posting the question. The answer is L =3/7

Explanation:

I initially thought that the 2, 9, 10, and 21 were separate terms so I divided 5^n on all of those. I looked again and realized that was not the case.

= ((2*3^n)/5^n+(9*5^n)/5^n)/((10*3^n)/5^n+(21*5^n)/5^n)

=((2*0)+(9*1))/((10*0)+(21*1))

= 9/21 = 3/7