You have the sequence s_n=\frac{3n-4n^3}{5n^2+2} and t_n=\cos(\frac{1}{n}). What conclusion can

ndimiimpercea2 2022-01-25 Answered
You have the sequence sn=3n4n35n2+2 and tn=cos(1n). What conclusion can you make about each of the sequences?
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Ydaxq
Answered 2022-01-26 Author has 12 answers
sn=3n4n35n2+2=3n4n5+2n2
limnsn=limn3n4n5+2n2
=05+0=
limnsn does not exists definitely so. That sn is a divergent sequence.
tn=cos(1n)
limntn=limncos(1n)=cos(1)=cos(0)=1
So that tn converges to 1
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