Given the infinite series: $$\sum^{\infty}_{n=1}\frac{1}{2n+3}$$ Determine whether this series converges.
The answer key used the integral test to determine that no, this series does not converge.
I came at this problem differently. I first tried using the comparison test with $\frac1n$ which was inconclusive. I then tried the limit comparison test – again with $\frac1n$. I got a limit of $\frac12$. Because this is a finite, positive number – the limit diverges.
As a beginner, I am simply unsure that my method was legitimate – after all – its a fifty fifty chance of getting it right:) So, I am asking here- did I find the answer using a legitimate method?
Best Answer
Yes, you used the limit comparison test correctly