Given the power series n=0 0 6n || 200+ 11/1/2 6 + 816 + O + 62 + 2x 6² x3 d xn d x * £ £ € - ( ¹ + 3 + 2 + 3 + +-) Find x³ 1+ dx 6n dx 6 n=0 62 63 64 by differentiating term by term. Write the first 5 terms below, simplifying any powers of -1. 63 + Jo... Write the series compactly using summation notation (if the series alternates, include the alternator separately): 64 + + 3r² 63 14 n=1 (Notice that since the constant term was dropped, we start the summation at n = 1.) Find the interval of convergence for the new series.

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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Given the power series
Find
0
d
dx
∞
n=0
xn
d
6n dx
-
xn
6n
||
1+
X
Jo. Jo.
+
+
x2
62
2x
+
n=0
by differentiating term by term.
Write the first 5 terms below, simplifying any powers of -1.
63 +
x
x²
1+ + + + +
6 62 63
x³
64
x4
Jog.
+
64
+
3.x
63
8
OT
+
Write the series compactly using summation notation (if the series alternates, include the alternator
separately):
امی است
n=1
(Notice that since the constant term was dropped, we start the summation at n= 1.)
Find the interval of convergence for the new series.
Transcribed Image Text:Given the power series Find 0 d dx ∞ n=0 xn d 6n dx - xn 6n || 1+ X Jo. Jo. + + x2 62 2x + n=0 by differentiating term by term. Write the first 5 terms below, simplifying any powers of -1. 63 + x x² 1+ + + + + 6 62 63 x³ 64 x4 Jog. + 64 + 3.x 63 8 OT + Write the series compactly using summation notation (if the series alternates, include the alternator separately): امی است n=1 (Notice that since the constant term was dropped, we start the summation at n= 1.) Find the interval of convergence for the new series.
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