sn = (((-1)^n)*n)/(2n - 1)
How would I determine the convergence or divergence of the sequence (sn) and find the limit if it exists?
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sn = (((-1)^n)*n)/(2n - 1)
How would I determine the convergence or divergence of the sequence (sn) and find the limit if it exists?
As this sequence has alternating signs it can only converge toQuote:
Originally Posted by bearej50
and so
must also converge to
:
as
so the original sequence does not converge.
CB
I would see if this has a limit by the ratio test:Quote:
^n}{2n-1})
(\frac{2n+1-2}{2n+1})=-(1+\frac{1}{n})(1-\frac{2}{2n+1})=-(1+\frac{1}{n}-\frac{2}{2n+1}-\frac{2}{n(2n+1)}))
but for the ratio test (I should have probably put this in before =S) we need to take the modulus.
Unfortunately, if the ratio test produces 1 the test doesn't hold. =S