and Vk are convergent series Vk) are convergent series and tl E(uk + vk) = L Uk k=1 k=1 Σ E(ur – « vk) = E Uk k=1 k=1 bove theorem to find the sum Prite your answer in the form of a redu

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
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Question
If uk and > Vk are convergent series, then 2(uk + vk) and
> (uk – vk) are convergent series and the sums of these series are
related by
E(uk + VR)
Σ
Uk + >
Uk
k=1
k=1
k=1
(uk – vr) = 2 u; –
Vk)
-Σ
Uk
-
k=1
k=1
k=1
Use the above theorem to find the sum of each series.
NOTE:
Write your answer in the form of a reduced improper fraction, if necessary.
1
5
(a) E
k2 – 1
k=2
10k-1
|
2k+2"
(b) 7-k3k+1
5k
k=1
Transcribed Image Text:If uk and > Vk are convergent series, then 2(uk + vk) and > (uk – vk) are convergent series and the sums of these series are related by E(uk + VR) Σ Uk + > Uk k=1 k=1 k=1 (uk – vr) = 2 u; – Vk) -Σ Uk - k=1 k=1 k=1 Use the above theorem to find the sum of each series. NOTE: Write your answer in the form of a reduced improper fraction, if necessary. 1 5 (a) E k2 – 1 k=2 10k-1 | 2k+2" (b) 7-k3k+1 5k k=1
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