Consider applying the Limit Comparison Test on S = ∑ k = 1 ∞ (...

fabianmartinOTQ

fabianmartinOTQ

Answered

2022-12-04

Consider applying the Limit Comparison Test on S = k = 1 ( 3 k 5 ( k 1 ) ( k + 1 ) )
a) Setup and calculate the limit in this test, comparing this series to k = 2 ( 1 k )
b) Interpret the result of this limit in this test.

Answer & Explanation

hayaniqWf

hayaniqWf

Expert

2022-12-05Added 10 answers

S = k = L 3 k 5 ( k 1 ) ( k + 1 ) = a k b R = 1 R
a) l t k a R b R = l t k 3 k 2 5 ( k 1 ) ( k + 1 ) = l t k 3 5 | 1 1 R | | 1 + 1 R | = 3 5
b) By limit compasion test, since b R is divergent
k = 2 3 k 5 ( k 1 ) ( k + 1 ) is divergent

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