Convergence Rule

G

Guest

Guest
Hi there, I have a convergence problem along the lines of:
1/1 + 1/2 + 1/3 +...+1/n = whatever (its not this problem btw)
I am just damned if I can remember what you're supposed to do to find a general convergence rule, its something to do with terms cancelling out and you get a general rule, if anyone could help, would be greatly appreciated.
Cheers
Josh
 
There are many different rules for testing convergence of series. The rules that apply to a particular series depend on that series. There is not, to my knowledge, one formula that "works" for every series.

Eliz.
 
No its not so much as a rule but a ways of manipulating the series to give you a general formula (I think)
Heres the problem:
Using partial fractions or otherwise, show that:
1/(1.3) + 1/(2.4) + 1/(3.5) ... + 1/N(N+2) = (1/2)(1 + 1/2 - 1/(N+1) - 1/(N+2))

Thats where I get stumped!
Josh
 
1/[N(N+2)] converts to partial fractions as [1/(2N)]−[1/(2(N+2))].
You can use this to find ‘collapsing sums’.
 
That's what I meant! The cancelling thing where there's a minus and things disappear! Top stuff.
Cheers man.
Josh
 
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