The sequence {Sn} of real numbers given by Sn = isa)a divergent sequenceb)a Cauchy sequencec)an oscillatory sequenced)not a Cauchy sequenceCorrect answer is option 'B'. Can you explain this answer?

Question

The sequence {Sn} of real numbers given by Sn =  isa)a divergent sequenceb)a Cauchy sequencec)an oscillatory sequenced)not a Cauchy sequenceCorrect answer is option 'B'. Can you explain this answer?

Answer

So n> is monotonically increasing Next, we will show that it is bounded.

⇒ n> is bounded. By the theorem's Every monotonic bounded sequence is convergent, Then n> is convergent.
By the Lemma, if n> is a convergent sequence of real numbers, Then n> is a Cauchy-sequence.

Answer

Can't we prove this by finding limit...?

how can we find the limit of lim sin(π/2^n)/n(n+1) where n approaches to infinity

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