1. Test the series below for convergence using the RootTest.
??n=1 (2n/7n+5)^n
The limit of the root test simplifies to lim n?? |f(n)| where
f(n)=
The limit is:
Based on this, the series
2. Multiple choice question. We want to use theAlternating Series Test to determine if the series:
??k=4 (?1)^k+2 k^2/?k5+3
converges or diverges.
We can conclude that:
- The Alternating Series Test does not apply because the terms ofthe series do not alternate.
- The Alternating Series Test does not apply because the absolutevalue of the terms do not approach 0, and the series diverges forthe 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 absolutevalue of the terms are not decreasing.
