+0  
 
0
96
1
avatar

1.

Determine all values of a for which \(\displaystyle\sum_{n=1}^{\infty}\left(\dfrac{2}{a}\right)^n \) converges. I believe this to be (2,inf)
2.

Determine all values of a for which \(\displaystyle\sum_{n=1}^{\infty}\left(\dfrac{2}{n}\right)^a \)  converges. I believe this to be (0,inf)

 Mar 31, 2021
 #1
avatar+420 
+1

1. Almost right; you forgot negative values wink

(just as a reminder, the sum \(\displaystyle\sum_{n=1}^{\infty}x^n\) where x is a constant only converges when \(-1  by the ratio test.)

So the answer would be \((-\infty, -2)\bigcup(2, \infty)\)

2. The sum \(\displaystyle\sum_{n=1}^{\infty}\left(\dfrac{y}{n}\right)^a\), where y is a constant, only converges when \(a>1\), so the answer is \((1, \infty)\)

 Mar 31, 2021

17 Online Users

avatar
avatar
avatar