consider the series:
∞
∑ (an)
n=1
where an: (n+3)^2n/(4n+5)^2n
using the root test, determine whether this series converges absolutely or conditionally or diverges
∞
∑ (an)
n=1
where an: (n+3)^2n/(4n+5)^2n
using the root test, determine whether this series converges absolutely or conditionally or diverges
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The title is stated incorrectly - to compute it, you would evaluate a number it is equal to, and you wouldn't use the root test to do it, which is to determine convergence or divergence.
To apply the root test, find the limit of the nth root of the nth term, which is just (n+3)^2 / (4n+5)^2 which approaches 1/16 in the limit.
The sum therefore converges absolutely.
(Conditional convergence is for alternating series when the alternating series converges but the series of the absolute values diverges.)
To apply the root test, find the limit of the nth root of the nth term, which is just (n+3)^2 / (4n+5)^2 which approaches 1/16 in the limit.
The sum therefore converges absolutely.
(Conditional convergence is for alternating series when the alternating series converges but the series of the absolute values diverges.)