- #1
azatkgz
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Homework Statement
Determine whether the series converges or diverges.
[tex]\sum_{n=1}^{\infty}\frac{1}{n^{1+\frac{1}{n}}}[/tex]
The Attempt at a Solution
[tex]\sum_{n=1}^{\infty}\frac{1}{nn^{\frac{1}{n}}}=\sum_{n=1}^{\infty}\frac{1}{ne^{\frac{1}{n}\ln n}}[/tex]
[tex]\lim_{n\rightarrow\infty}\frac{\ln n}{n}=0[/tex]
[tex]\sum_{n=1}^{\infty}\frac{1}{ne^0}=\sum_{n=1}^{\infty}\frac{1}{n}[/tex]
Series diverges.