Consider the series 1 k²(k+1) k=1 (i) Use Test for Divergence to check if the sequence is convergent or divergent. (ii) Use Ratio Test to check if the sequence is convergent or divergent. (iii) Use Limit Comparison Test to check if the sequence is convergent or divergent. (iv) Use Abel's Test to check if the sequence is convergent or divergent.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 82E
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Consider the series
Σ
k=1
1
k²(k+1)
(i) Use Test for Divergence to check if the sequence is convergent or divergent.
(ii) Use Ratio Test to check if the sequence is convergent or divergent.
(iii) Use Limit Comparison Test to check if the sequence is convergent or divergent.
(iv) Use Abel's Test to check if the sequence is convergent or divergent.
Transcribed Image Text:Consider the series Σ k=1 1 k²(k+1) (i) Use Test for Divergence to check if the sequence is convergent or divergent. (ii) Use Ratio Test to check if the sequence is convergent or divergent. (iii) Use Limit Comparison Test to check if the sequence is convergent or divergent. (iv) Use Abel's Test to check if the sequence is convergent or divergent.
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