If L uk and > Uk are convergent series, then > (uk + Vk) and Συ 2(uk – vk) are convergent series and the sums of these series are - related by 00 (Uk + vk) > uk + k=1 k=1 k=1 00 00 00 2(uk – vk) = 2 u* - 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 (a) 1 1 1 +... + 72 1 + 22 2k 00 ( b) Σ 1 12k k(k + 1) k=1
If L uk and > Uk are convergent series, then > (uk + Vk) and Συ 2(uk – vk) are convergent series and the sums of these series are - related by 00 (Uk + vk) > uk + k=1 k=1 k=1 00 00 00 2(uk – vk) = 2 u* - 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 (a) 1 1 1 +... + 72 1 + 22 2k 00 ( b) Σ 1 12k k(k + 1) k=1
Chapter9: Sequences, Probability And Counting Theory
Section9.4: Series And Their Notations
Problem 10TI: Determine whether the sum of the infinite series is defined. 24+(12)+6+(3)+
Related questions
Question
Transcribed Image Text:If L uk and Vk are convergent series, then (Uk + Vk) and
E(uk – vk) are convergent series and the sums of these series are
related by
00
2(uk + VR) = E Uz +
2 uk +
Uk
k=1
k=1
00
00
2(uk – vk) :
Uk) = E
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
(a)
1
+
22
1
+ ... +
1
1
+
72
...
Σ
1
1
(b)
12k
k(k + 1),
k=1
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage