If u; and > Vk are convergent series, then > (ux + vk) and (uk – vk) are convergent series and the sums of these series are related by E(uk + vk) = uk + Lvk k=1 k=1 k=1 E(uk – vk) = LUk -Evk 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. (a) 5 1 1 + + 82 1 1 + + 2k 8 22 1 1 (b) 2 13k k(k +1), k=1 ||
If u; and > Vk are convergent series, then > (ux + vk) and (uk – vk) are convergent series and the sums of these series are related by E(uk + vk) = uk + Lvk k=1 k=1 k=1 E(uk – vk) = LUk -Evk 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. (a) 5 1 1 + + 82 1 1 + + 2k 8 22 1 1 (b) 2 13k k(k +1), k=1 ||
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
Transcribed Image Text:If 2 uk and > vk are convergent series, then > (uk + vk) and
2(u – vk) are convergent series and the sums of these series are
related by
2(uk: + Vk) = LUk +
Uk
k=1
k=1
k=1
E(uk – vk) = >uk ,
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
1
+
82
1
(a) (;
+
bk
8
22
2k
1
1
(b) )
13k
k(k + 1),
k=1
||
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