Hey guys, Can't get this Q out. T{n}=(1/n)-(1/[n+1]) Give a formula for T{1}+T{2}+...+T{n} Thanks.
shaon0 ... Joined Mar 26, 2008 Messages 2,029 Location Guess Gender Male HSC 2009 Mar 10, 2009 #1 Hey guys, Can't get this Q out. T{n}=(1/n)-(1/[n+1]) Give a formula for T{1}+T{2}+...+T{n} Thanks.
D Drongoski Well-Known Member Joined Feb 22, 2009 Messages 4,245 Gender Male HSC N/A Mar 10, 2009 #2 T{1} + T{2} + T{3} + ..... + T{n-1} + T{n} = (1/1 - 1/2) + (1/2 -1/3) + (1/3 - 1/4) + .... + (1/(n-1) - 1/n) + (1/n - 1/(n+1) = 1 + 0 + 0 + . . . . . + 0 - 1/(n + 1) = 1 - 1/(n + 1) = n/(n + 1)
T{1} + T{2} + T{3} + ..... + T{n-1} + T{n} = (1/1 - 1/2) + (1/2 -1/3) + (1/3 - 1/4) + .... + (1/(n-1) - 1/n) + (1/n - 1/(n+1) = 1 + 0 + 0 + . . . . . + 0 - 1/(n + 1) = 1 - 1/(n + 1) = n/(n + 1)
shaon0 ... Joined Mar 26, 2008 Messages 2,029 Location Guess Gender Male HSC 2009 Mar 10, 2009 #3 Drongoski said: T{1} + T{2} + T{3} + ..... + T{n-1} + T{n} = (1/1 - 1/2) + (1/2 -1/3) + (1/3 - 1/4) + .... + (1/(n-1) - 1/n) + (1/n - 1/(n+1) = 1 + 0 + 0 + . . . . . + 0 - 1/(n + 1) = 1 - 1/(n + 1) = n/(n + 1) Click to expand... ah cool, thanks. I found the mistake that i made.
Drongoski said: T{1} + T{2} + T{3} + ..... + T{n-1} + T{n} = (1/1 - 1/2) + (1/2 -1/3) + (1/3 - 1/4) + .... + (1/(n-1) - 1/n) + (1/n - 1/(n+1) = 1 + 0 + 0 + . . . . . + 0 - 1/(n + 1) = 1 - 1/(n + 1) = n/(n + 1) Click to expand... ah cool, thanks. I found the mistake that i made.
