Question

Find the limit of the sequence or why it diverges?

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

Answer 1

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`