3. Prove from first principles that the following sequences converge. (Hint: your first job is to figure out, informally, what the limit is in each case.) an = Cn = n+1 n+ 2' { 400/n -1/(400m²) n odd n even " 0 bn = dn = 5n 4n²-3' { "/(1+ 7 n/(1+n²) 1≤ n ≤ 900 n> 901
3. Prove from first principles that the following sequences converge. (Hint: your first job is to figure out, informally, what the limit is in each case.) an = Cn = n+1 n+ 2' { 400/n -1/(400m²) n odd n even " 0 bn = dn = 5n 4n²-3' { "/(1+ 7 n/(1+n²) 1≤ n ≤ 900 n> 901
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 33E
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Transcribed Image Text:3. Prove from first principles that the following sequences converge. (Hint: your first job
is to figure out, informally, what the limit is in each case.)
an =
Cn =
n+1
n+ 2'
{
n odd
400/n
-1/(400m²) n even
"
0
bn
=
dn =
5n
4n²-3'
{ "/(1+
7
n/(1+n²) 1≤n ≤ 900
n> 901
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