How do you determine the convergence or divergence of $Sigma sin(((2n-1)pi)/2)$ from $[1,oo)$ ?

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Answer 1 · 2017-01-16T20:06:37

Not convergent.

$((2n-1)pi)/2=npi-pi/2$

so $sin(npi-pi/2)=-cos(npi) = -(-1)^n$

Finally

$sum sin(((2n-1)pi)/2) = -sum(-1)^n$ which is not convergent

How do you determine the convergence or divergence of Sigma sin(((2n-1)pi)/2)Sigma sin(((2n-1)pi)/2) from [1,oo)[1,oo)?