How do you test for convergence given #Sigma (-1)^n(1-1/n^2)# from #n=[1,oo)#?

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Answer 1 · 2017-01-27T09:38:26

The series:

#sum_(n=1)^oo (-1)^n (1-1/n^2)#

is not convergent.

A necessary condition for any series to converge is that the general term of the succession is infinitesimal, that is:

#lim_(n->oo) a_n = 0#

In our case we have:

#lim_(n->oo) (1-1/n^2) = 1#

and so:

#lim_(n->oo) a_n = lim_(n->oo) (-1)^n(1-1/n^2)#

is indeterminate.