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Suppose that a power series 00 8(x) = bn x" %3D n=0 00 has the radius of convergence p > 0 , all b, are positive, and that > diverges to ∞. Then show that f(x)/g(x) converges to a as x → p- for any ,bnp" power series f(x) = L anx" %D n=0 such that a,/b, converges to a as n → ∞,

Suppose that a power series 00 8(x) = bn x" %3D n=0 00 has the radius of convergence p > 0 , all b, are positive, and that > diverges to ∞. Then show that f(x)/g(x) converges to a as x → p- for any ,bnp" power series f(x) = L anx" %D n=0 such that a,/b, converges to a as n → ∞,

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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Suppose that a power series 00 8(x) = L b, x" n=0 00 has the radius of convergence p > 0 , all b, are positive, and that£ diverges to ∞. Then show that f(x)/g(x) converges to a as x → p- for any bnp" n=0 power series 00 f(x) = L anx" n=0 such that a„/b, converges to a as n → ∞,.
Transcribed Image Text:Suppose that a power series 00 8(x) = L b, x" n=0 00 has the radius of convergence p > 0 , all b, are positive, and that£ diverges to ∞. Then show that f(x)/g(x) converges to a as x → p- for any bnp" n=0 power series 00 f(x) = L anx" n=0 such that a„/b, converges to a as n → ∞,.
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