- #1

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## 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/3

^{1+3n}

n=1

## Homework Equations

## The Attempt at a Solution

∞

∑ n/3

^{1+3n}= n/(3⋅27

^{n})

n=1

lim |(n+1)/(3⋅27

^{n+1}) / (n/3 *27

^{n})|

n→∞

= lim |(n+1)/n| * (1/27)

n→∞

= 1 * 1/27

=1/27 < 1

Convergent by Ratio Test