Question

so i have to match a series with graph of its sequence of partial sum. how do i determine whether the series converges or diverges

Answer 1

if the graph of the prtial sum appears to be approaching a number (or limit as it goes to infinity) then the series is converging to that limit. Kind of like how 1/x appears to be approaching zero. Different sums go to either a distinct number or they oscillate, or get infinitely larger . In those cases where there is no distinctive limit, then the series diverges.

Answer 2

I think too that if you are dealing with the infinite series itself and not the partial sums of the sequence, if the limit does exist for the series, then the series diverges. I'm pretty sure that is the case, but there are so many rules and so many different seeries and sequences, it is hard to remember. Pay attention to what literature you have and the examples in the chapter though,. When judging by the graph, the previous not should work.