Question

1. Test the series below for convergence using the Root Test.
∞∑n=1 (4n/10n+1)^n
The limit of the root test simplifies to lim n→∞ |f(n)| where
f(n)=
The limit is:    
Based on this, the series

• Diverges
• Converges

2. We want to use the Alternating Series Test to determine if the series:

∞∑k=4 (−1)^k+2 k^2/√k^5+3

converges or diverges.
We can conclude that:

• The Alternating Series Test does not apply because the terms of the series do not alternate.
• The Alternating Series Test does not apply because the absolute value of the terms do not approach 0, and the series diverges for the same reason.
• The series converges by the Alternating Series Test.
• The series diverges by the Alternating Series Test.
• The Alternating Series Test does not apply because the absolute value of the terms are not decreasing.

Answer 1