Question

How do you test this series for convergence or divergence? 4/7 - 4/8 + 4/9 - 4/10 + 4/11 - .....

Answer 1

First find the sum notation form of the series:

\[\sum_{1}^{\infty}(-1)^{n+1}(4/(n+6))\]

Since it's an alternating, you can use the Alternating Series Theorem.
i)An is positve
ii)An+1 < An
iii) \[\lim_{n \rightarrow \infty} 4/(n+6) \]

Prove all three conditions are true and it's convergent

Answer 2

limit = 0

Answer 3

ok thanks =)