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in (nx) be a sequence of functions. Show that the series sin Problem 2 Let fn(x) = n2 sin (nx) E fa (x) = £ 00 00 %3D n2 n=1 n=1 converges for all values of x but the series of derivatives E1 fh(x) diverges when x=2kt where k is an integer. This problem gives us an example where for infinite sums, the derivative of a sum is not the sum of the derivatives.

in (nx) be a sequence of functions. Show that the series sin Problem 2 Let fn(x) = n2 sin (nx) E fa (x) = £ 00 00 %3D n2 n=1 n=1 converges for all values of x but the series of derivatives E1 fh(x) diverges when x=2kt where k is an integer. This problem gives us an example where for infinite sums, the derivative of a sum is not the sum of the derivatives.

Advanced Engineering Mathematics
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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Problem 2 Let fn(x) = Sm ) be a sequence of functions. Show that the series sin (nx) E fn (x) = E 6) = Ë n2 n=1 n=1 converges for all values of x but the series of derivatives E1 f(x) diverges when.x= 2kt where k is an integer. This problem gives us an example where for infinite sums, the derivative of n=1 Jn a sum is not the sum of the derivatives.
Transcribed Image Text:Problem 2 Let fn(x) = Sm ) be a sequence of functions. Show that the series sin (nx) E fn (x) = E 6) = Ë n2 n=1 n=1 converges for all values of x but the series of derivatives E1 f(x) diverges when.x= 2kt where k is an integer. This problem gives us an example where for infinite sums, the derivative of n=1 Jn a sum is not the sum of the derivatives.
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