- #1
Of Mike and Men
- 54
- 3
Homework Statement
I was watching a PatrickJMT video on ratio test and he gave this problem. I solved it before he did, and he got that it was divergent. He didn't simplify it initially, so our methods of approach are different. Did I do something wrong? I checked my calculator to make sure all my simplifications were correct. So I'm assuming I did something near the limit portion that was incorrect (if at all). Thanks
∞
∑ n/31+3n
n=1
Homework Equations
The Attempt at a Solution
∞
∑ n/31+3n = n/(3⋅27n)
n=1
lim |(n+1)/(3⋅27n+1) / (n/3 *27n)|
n→∞
= lim |(n+1)/n| * (1/27)
n→∞
= 1 * 1/27
=1/27 < 1
Convergent by Ratio Test