Find a formula for the nth partial sum of each series and use it to find the series' sum if the series converges. 2 +.. 2 (i) 2+ 3 9 (ii) 100 +...+ 27 9. + 9 3n-1 + (100)2 9 + (100)3 9 +... ... 100" 1 1 (iii) 1 – + 4 1 +...+ 8. (-1)"-1 +... - 2n-1 (iv) 1–2+4 – 8+ ...+(-1)"-2"-1 + ... 1 + + 3.4 1 1 + 4.5 1 (v) 2.3 + (n + 1)(n + 2) (vi) 1.2 + + 3.4 + п(п + 1) + ... 2.3

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Find a formula for the nth partial sum of each series and use it to find the
series' sum if the series converges.
2
+..
2
(i) 2+
3
9
(ii)
100
+...+
27
9.
+
9
3n-1
+
(100)2
9
+
(100)3
9
+...
...
100"
1
1
(iii) 1 –
+
4
1
+...+
8.
(-1)"-1
+...
-
2n-1
(iv) 1–2+4 – 8+ ...+(-1)"-2"-1 + ...
1
+
+
3.4
1
1
+
4.5
1
(v)
2.3
+
(n + 1)(n + 2)
(vi)
1.2
+
+
3.4
+
п(п + 1)
+
...
2.3
Transcribed Image Text:Find a formula for the nth partial sum of each series and use it to find the series' sum if the series converges. 2 +.. 2 (i) 2+ 3 9 (ii) 100 +...+ 27 9. + 9 3n-1 + (100)2 9 + (100)3 9 +... ... 100" 1 1 (iii) 1 – + 4 1 +...+ 8. (-1)"-1 +... - 2n-1 (iv) 1–2+4 – 8+ ...+(-1)"-2"-1 + ... 1 + + 3.4 1 1 + 4.5 1 (v) 2.3 + (n + 1)(n + 2) (vi) 1.2 + + 3.4 + п(п + 1) + ... 2.3
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