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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

  • Diverges
  • Converges

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.

Solutions

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