If ak = 1/k-1/(k+1), then find out the summation of a2 to a100?

(Here k, 2 & 100 are suffixes)

a2=3

a3=2

a4=5/3 and so on i dont see any pattern how to find the summation ,is there any direct formula

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- Aug 19th 2009, 11:05 AMarunachalam.ssummation
If ak = 1/k-1/(k+1), then find out the summation of a2 to a100?

(Here k, 2 & 100 are suffixes)

a2=3

a3=2

a4=5/3 and so on i dont see any pattern how to find the summation ,is there any direct formula - Aug 19th 2009, 11:12 AMChris L T521
- Aug 19th 2009, 11:22 AMarunachalam.s
1/k-1/(k+1)=k+1/k-1 how did u get 1/k-1/k+1

- Aug 19th 2009, 11:45 AMChris L T521
The way you posted your question could be interpreted in many ways...

or or .

To make it easier for us to answer your future questions, please learn some basic . See here for help. - Aug 19th 2009, 11:47 AMPim
Order of operations.

First divide, then subtract.

Also, for the sanity of all of us, use LaTex, or at least use brackets.

As I now see it, you could mean either one of these two:

1/k-1/(k+1) =

OR

(1/(k-1))/(k+1) =

- Aug 19th 2009, 12:07 PMarunachalam.s
__i cant understand__

1/(k-1)/(k+1) lets put k=2 now this yields 1/(2-1)/(2+1)=1/3 which is not equal to (2+1)/(2-1)=3 i still cant understand how both the fractions r equal now if we take 1/k-1/(k+1) = 1/2-1/(3)=(3-2)/6 which is equal t0 1/6 now this both r not equal how u say all fractions are equal ..