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As a preparation for what we ll do next week, read over your old calculus text about infinite series and power series. (a) Prove that the real power series (-1)"r²" n! for converges every real r.

As a preparation for what we ll do next week, read over your old calculus text about infinite series and power series. (a) Prove that the real power series (-1)"r²" n! for converges every real r.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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The questions are below. This is math 3001 Real Analysis II

(3) As a preparation for what we'll do next week, read over your old calculus text about infinite series and power series. (a) Prove that the real power series (-1)"z2" converges for every real n! r. (b) Prove that the real power series n!r" converges for only a = 0. (c) Pick your favourite real power series a,a". Show that for this series, the equivalence %3D 30 Σ ana" converges + > na,r"- converges. n=0 holds, with the possible exception of at most two real values of a,
Transcribed Image Text:(3) As a preparation for what we'll do next week, read over your old calculus text about infinite series and power series. (a) Prove that the real power series (-1)"z2" converges for every real n! r. (b) Prove that the real power series n!r" converges for only a = 0. (c) Pick your favourite real power series a,a". Show that for this series, the equivalence %3D 30 Σ ana" converges + > na,r"- converges. n=0 holds, with the possible exception of at most two real values of a,
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