1.1.1 Prove that if lim,0 nPu, =A 1, the series n="n converges. %3D A 0, the series diverges. (The test fails for A 0.) (b) Prove that if lim,0o nun = A These two tests, known as limit tests, are often convenient for establishing the convergence of a series. They may be treated as comparison tests, comparing with En-4. 1<4< p.

1.1.1 Prove that if lim,0 nPu, =A 1, the series n="n converges. %3D A 0, the series diverges. (The test fails for A 0.) (b) Prove that if lim,0o nun = A These two tests, known as limit tests, are often convenient for establishing the convergence of a series. They may be treated as comparison tests, comparing with En-4. 1<4< p.

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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Question

book name-Mathematical Methods for Physicists (7th)-Arfken-Weber-Harris-Harris

1.1.1
Prove that if lim,0 nPu, =A<o0, p> 1, the series n="n converges.
%3D
A 0, the series diverges. (The test fails for A 0.)
(b) Prove that if lim,0o nun = A
These two tests, known as limit tests, are often convenient for establishing the
convergence of a series. They may be treated as comparison tests, comparing with
En-4. 1<4< p.

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