. (a) Find a formula for the n th partial sum of each series given below and use it to find the sum of the series if the series converges. 2 2 (i) 2+ 3 + 3n-1 + ..... 9. 27 9. 9. 9. (ii) 100 1002 1003 + .... 100"
. (a) Find a formula for the n th partial sum of each series given below and use it to find the sum of the series if the series converges. 2 2 (i) 2+ 3 + 3n-1 + ..... 9. 27 9. 9. 9. (ii) 100 1002 1003 + .... 100"
Chapter9: Sequences, Probability And Counting Theory
Section9.4: Series And Their Notations
Problem 4SE: How is finding the sum of an infinite geometric series different from finding the nth partial sum?
Related questions
Question
![1. (a) Find a formula for the n th partial sum of each series given below and use it to find the sum of
the series if the series converges.
2
2
2
2
+
3n-1
9
+
100"
(i) 2+
3
+
27
9.
9
9
(ii)
100
1002
1003
(b) Find the sum of each series below using the simple fractionation method.
1
40n
(i)
(ii)
Vn + 1
(2n – 1)2(2n + 1)2
n=1
n=:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce0b7b5f-4f37-434f-ba8f-2945bd276c47%2F3af064fa-e1fe-40c1-b6e3-d82969a6a853%2Fp6tumwf_processed.png&w=3840&q=75)
Transcribed Image Text:1. (a) Find a formula for the n th partial sum of each series given below and use it to find the sum of
the series if the series converges.
2
2
2
2
+
3n-1
9
+
100"
(i) 2+
3
+
27
9.
9
9
(ii)
100
1002
1003
(b) Find the sum of each series below using the simple fractionation method.
1
40n
(i)
(ii)
Vn + 1
(2n – 1)2(2n + 1)2
n=1
n=:
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