Given sequences S_n=\frac{3n-4n^{3}}{5n^{2}+2} and t_n=\cos(\frac{1}{n}).What conclusion we can make about each of the sequences?

DofotheroU

DofotheroU

Answered question

2021-06-08

Given sequences Sn=3n4n35n2+2 and tn=cos(1n).
What conclusion we can make about each of the sequences?

Answer & Explanation

Usamah Prosser

Usamah Prosser

Skilled2021-06-09Added 86 answers

Sn=3n4n35n2+2
=3n4n5+2n2
limn to Sn=limn to 3n4n5+2n2
=05+0= limnSn does not exists binitely
So that sn is a divergent sequence
tncos(1n)
limntn=limncos(1n)=cos(1)=cos(0)=1
So that tn converges to 1

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