11.5 Infinite Sequences & Series
Question #2 (Medium): Converging Series Against Alternating Series Test
For an alternating series given as ∑ , it can be written as a more obvious alternating series like
∑ ( )
Alternating series test states that the series converges if it meets two conditions:
1) for all
Instead of working with n+1 and n, take the first derivative of the series function and see if .
Only when the first derivative is negative, it is a decreasing function for all .
Test the series against the alternating series test for convergence or divergence.
Given the alternating series, [ ( )]