How do you determine if the series the converges conditionally, absolutely or diverges given $Sigma ((-1)^(n))/(lnn)$ from $[1,oo)$ ?

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Answer 1 · 2016-12-09T15:43:54

The series is convergent.

We have that $a_n = ((-1)^n)/(log(n))$ It is an alternating series.

This series is converget if

1) $lim_(n->oo) a_n = 0$
2) $abs(a_(n+1)) < abs(a_n)$

This series accomplishes both requirements so it is convergent.

Attached a plot of $S(n)=sum_(k=2)^n((-1)^k)/(logk)$

enter image source here

How do you determine if the series the converges conditionally, absolutely or diverges given Sigma ((-1)^(n))/(lnn)Sigma ((-1)^(n))/(lnn) from [1,oo)[1,oo)?