Question

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Answer 1

@Valpey I dont think we got it right the first time.

Answer 2

conditional convergence.

Answer 3

and this is because when we take the abs value it doesnt converge right?

Answer 4

Alternating sequences of terms with strictly decreasing absolute values converge to a finite sum. If the absolute values summed to a converged sum also, that would be absolutely convergent. This does not, though since \[\frac{1}{\sqrt{n}}>\frac{1}{n} and \sum_{n=1}^{\infty}\frac{1}{n}=\infty\]

Answer 5

I meant\[\frac{1}{\sqrt{n}}\ge\frac{1}{n}\forall \ n\]