3. For each of the following sequences, prove, using an ɛ,no argument that the sequence converges to the given limit p; that is, given ɛ > 0, determine no such that |pn– p| < ɛ for all n > no- Зп+5 2n+7 } ;P = (b) {},p= } 6n- (e) {},p = } n²+1 2n2 (d) {1-"},p=1 (-1)" (e) {/n+I-\m},p = 0

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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3. For each of the following sequences, prove, using an ɛ,no argument that the sequence
converges to the given limit p; that is, given ɛ > 0, determine no such that |Pn – p| < E
for all n > no-
(a) {},p=
Зп+5
2n+7
(b) {},p= }
2n+5
6n-
(e) {},p = }
(d) {1–},p=1
n²+1
2n2
(e) {Vn+1-\m},p=0
Transcribed Image Text:3. For each of the following sequences, prove, using an ɛ,no argument that the sequence converges to the given limit p; that is, given ɛ > 0, determine no such that |Pn – p| < E for all n > no- (a) {},p= Зп+5 2n+7 (b) {},p= } 2n+5 6n- (e) {},p = } (d) {1–},p=1 n²+1 2n2 (e) {Vn+1-\m},p=0
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