Discuss the convergence or divergence of the following sequence{an} an= {(n+1)/2n}(1-1/n)

Asked by Chetan | 4th Nov, 2012, 06:27: PM

Expert Answer:

The series an= [(n+1)/2n](1-1/n)
 
an= [1/2 + 1/2n](1-1/n)
As n tends towards infinity, 1/n tends towards zero
so the above value becomes
 
an= [1/2 + 0](1-0) = 1/2
 
which is finite and fixed.
 
Hence the series converges.

Answered by  | 8th Nov, 2012, 05:09: PM

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