does this series converge or diverge?
n = 2 E infinity
2/(n^2 -1)
..i've attempted to solve this, and i know the answer is 3/2
just not sure why i could not divide the numerator and denominator by the largest exponent in the denominator (n^2). is that because its not in the form of infininty/infinity?
also, tried using summation notation, it did not work out.
i know it can't be the harmonic series because that would diverge.
need some help please.
to find the sum, you can realize that you have a telescoping sum. note that
write out some of the terms of the series (be sure to include the last few terms as well, that is, say, the (n - 2)th term, the (n - 1)th term, the nth term). try to see a pattern of what cancels out and come up with an expression for what's left. then let and you should get your result
Okay, thanks for the help, i can't used the comparison test because i haven't learned it yet.
however i can use the telescoping series test, is that the same as the collapsing series?
also.. i've attached an image of what work i've done, I apoligize it is very messy, sorry was in a hurry.
btw, i see how the only terms of 1/2 and 1 are left only. but what happened to the (1/n-1) - (1/n+1) do those cancel out completely?
we used partial sums here to split the fraction up then?
thanks alot.
i don't know. don't think i've heard the term "collapsing series" before.
where's the image?also.. i've attached an image of what work i've done, I apoligize it is very messy, sorry was in a hurry.
this is why i told you to write out some terms. you'd realize that the (n - 2)th term cancels the , but the stays. you'd have to take the limit as to get the answerbtw, i see how the only terms of 1/2 and 1 are left only. but what happened to the (1/n-1) - (1/n+1) do those cancel out completely?
i used partial fractions decomposition to get the two fractionswe used partial sums here to split the fraction up then?