2. Prove from first principles (that is, give a proof following the form given in the original definition of convergence of a sequence) 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 { 400 I bn dn - - 5n 4n²-3' {n/(1+²) 15259000 n>

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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2. Prove from first principles (that is, give a proof following the form given in the original
definition of convergence of a sequence) 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/(400n²)
-{400
n odd
n even
X
bn
=
5n
4n²-3'
dn={n/+n) 1<n<900
7
n>
Transcribed Image Text:2. Prove from first principles (that is, give a proof following the form given in the original definition of convergence of a sequence) 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/(400n²) -{400 n odd n even X bn = 5n 4n²-3' dn={n/+n) 1<n<900 7 n>
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