In: Math
1. Test the series below for convergence using the Root
Test.
∞∑n=1 (2n/7n+5)^n
The limit of...
1. Test the series below for convergence using the Root
Test.
∞∑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 the
Alternating 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 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.