(a) Prove the convergence or divergence of each of the following series: 1! 2! 3! (i) + + +. + n! 2n + 1 +... 2+1 22 +1 23+1 (ii) 1 - 5 - 1 3 + (-1)"-1 2n 1 - +...

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(a) Prove the convergence or divergence of each of the following series:
1!
2!
3!
(i)
+
+
+. +
n!
2n + 1
+...
2+1
22 +1
2³ +1
1
(-1)"-1
(ii)
1
+
+
+...
3 5
2n-1
(b) Show that the interval of convergence of the series
2n-12-1
(4n - 3)²
n=1
1
-
sos
<
1
√2
√2
-
is given by
Transcribed Image Text:(a) Prove the convergence or divergence of each of the following series: 1! 2! 3! (i) + + +. + n! 2n + 1 +... 2+1 22 +1 2³ +1 1 (-1)"-1 (ii) 1 + + +... 3 5 2n-1 (b) Show that the interval of convergence of the series 2n-12-1 (4n - 3)² n=1 1 - sos < 1 √2 √2 - is given by
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