3. Let {an} be a sequence of real number. Suppose that the power series on R below > an(x – a)" n=0 is converge absolutely on some set I C R. Suppose that the sequence { converge to 0. Then, n=0 ] = R.

3. Let {an} be a sequence of real number. Suppose that the power series on R below > an(x – a)" n=0 is converge absolutely on some set I C R. Suppose that the sequence { converge to 0. Then, n=0 ] = R.

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

Identify if the following statement is true or false. If the statement is true, then prove. Otherwise, if the statement is false, then give a counterexample. (Note: short and precise proofs only, no need for lengthy ones with so many explanations)

3. Let {an} be a sequence of real number. Suppose that the power series on IR below
00
> an (x – a)"
n=0
is converge absolutely on some set I C R. Suppose that the sequence
converge
n=0
to 0. Then,
{
an
I = R.

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