- #1
Al3x L3g3nd
- 14
- 1
Homework Statement
Does the series
[tex]
\Big( \sum_{n=1}^\infty\frac{1}{(3^n)*(sqrtn)} \Big)
[/tex]
Converge or Diverge? By what test?
Homework Equations
1/n^p
If p<1 or p=1, the series diverges.
If p>1, the series converges.
If bn > an and bn converges, then an also converges.
The Attempt at a Solution
I use 1/(sqrtn) since it is bigger than 1/((3^n)(sqrtn)).
Since sqrtn is n^1/2 I use the p test.
Since 1/2<1, the series 1/sqrtn diverges and so does the original.
This is wrong
The answer uses 1/3^n as the comparison and it just says that it converges with no explanation.
Also, the ratio test was used and it converged.
Why doesn't my reasoning work?