6. Find A and B such that for all i 2 2 A B %3D 2 - 1 i-1 i+1' | and use this identity to express the partial sum S, = E2 2/(i² – 1) of the series Σ n2 - 1 n22

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 50E
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6. Find A and B such that for all i > 2
A
22 - 1
i - 1
i +1'
and use this identity to express the partial sum S,
2 2/(i? – 1) of the series
Σ
n2 – 1
n22
as a telescoping sum. Use this telescoping sum to show that the series is convergent,
and find its sum.
ibono on svi9
timil ods hed to ii bs tao3
()
od y la ol s bohaoqu ni oi 00
ib gvno lleh010001
l ro sd to heog
dhabod b ga
odi die
lw o
000-100+10
Transcribed Image Text:6. Find A and B such that for all i > 2 A 22 - 1 i - 1 i +1' and use this identity to express the partial sum S, 2 2/(i? – 1) of the series Σ n2 – 1 n22 as a telescoping sum. Use this telescoping sum to show that the series is convergent, and find its sum. ibono on svi9 timil ods hed to ii bs tao3 () od y la ol s bohaoqu ni oi 00 ib gvno lleh010001 l ro sd to heog dhabod b ga odi die lw o 000-100+10
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