Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Consider the following series:

$$\sum_{n=1}^{\infty} \frac{3^{2^n}}{2^{3^n}}$$

I believe that this series converges, but I don't know how to prove this.

Thanks in advance!

share|improve this question
4  
Try the ratio test... –  Sanath Feb 14 at 2:08

1 Answer 1

Let $a_n=3^{2^n}/2^{3^n}$. Since $\lim_{n\rightarrow\infty}a_{n+1}/a_n=\lim_{n\rightarrow\infty}3^{2^n}4^{-3^n}=0$, from D' Alembert's theorem we know the sum of $a_n$ is convergence.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.