Then sequence defined asa)divergesb)Convergesc)oscillatesd)None of theseCorrect answer is option 'B'. Can you explain this answer?

Question

Then sequence <sn> defined asa)divergesb)Convergesc)oscillatesd)None of theseCorrect answer is option 'B'. Can you explain this answer?

Answer

Here, we have n> such that

Let n> & 2 _n–1> be the two subsequences of the sequence n> such that

Both the sequences n> & 2n+1> converges to he same limit 0. Hence the sequences n> Converges to 0.

Answer

Converges, as limit n-> infinity, sn->0

Answer

This is alternating series also converge to 0 so option b is correct