2) Show that if an → a then |an a. Is the converse true? Show that or give an example. An + an+1 + an+2 lim an. 3) If an is convergent, show that lim n400

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Hoping to get some help on question #2.
2n + 1
1) Use e – N to prove lim
n0 5n + 2
2) Show that if an → a then |an →a. Is the converse true? Show that or give an example.
An + an+1 + An+2
3) If an is convergent, show that lim
lim an.
3
4) Prove that the limit of the
sequence
V2, V2v2, /2/2v2,
2V2/2v2.-.
exists, and find it
5 + 2an
= 1 and an+1 =
An 2 1. Show that an converges, and find its limit.
5) A sequence an is defined by a1
4
Transcribed Image Text:2n + 1 1) Use e – N to prove lim n0 5n + 2 2) Show that if an → a then |an →a. Is the converse true? Show that or give an example. An + an+1 + An+2 3) If an is convergent, show that lim lim an. 3 4) Prove that the limit of the sequence V2, V2v2, /2/2v2, 2V2/2v2.-. exists, and find it 5 + 2an = 1 and an+1 = An 2 1. Show that an converges, and find its limit. 5) A sequence an is defined by a1 4
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