test the convergence of sigma 2n-1÷n(n+1)(n+2)
Answer (1)
23rd Dec, 2019
We have a(n)= 2n-1/n(n+1)(n+2).
Now we have to check the convergence.
At first take that it converges and the limit is 0.
Hence |2n-1/n(n+1)(n+2)|<2/(n+1)(n+2)<2/n^2
Then our n(e)=[√(2/e)]+1.
Hence for all e>0 there exist a natural no n(e)
Such that |a(n)-0|<e for all n>n(e).
Hence the sequence a(n) is convergent
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