Series converge or diverge?

[kddd1232]

This seems like can be done with root or ratio test, but I suck at algebra so I'm stuck finding the limit, any help?Thanks!

 

[LCKurtz]

View attachment 12592 This seems like can be done with root or ratio test, but I suck at algebra so I'm stuck finding the limit, any help?Thanks!

Maybe try comparison? You might start with [MATH]2^k - 1 \le 2^k[/MATH] and [MATH]k^k + 1 \ge k^k[/MATH].

 

[pka]

View attachment 12592 This seems like can be done with root or ratio test, but I suck at algebra so I'm stuck finding the limit, any help?Thanks!

Surely you realize that \(\displaystyle \frac{2^k-1}{k^k+1}\le \frac{2^k}{k^k}\), WHY?
What can you do with that?