SOLUTION: (1/1*2)+(1/2*3)+(1/3*4)+.........find the sum of n terms of the given series?

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Question 320727: (1/1*2)+(1/2*3)+(1/3*4)+.........find the sum of n terms of the given series?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use a substitution,
1%2F%28i%28i%2B1%29%29=1%2Fi-1%2F%28i%2B1%29
So then

1%2F%281%2A2%29%2B1%2F%282%2A3%29%2B1%2F%283%2A4%29+...1%2F%28n%28n%2B1%29%29=(1%2F1%2B1%2F2%2B1%2F3%2B1%2F4+...+1%2Fn)-(1%2F2%2B1%2F3%2B1%2F4+...+1%2Fn%2B1%2F%28n%2B1%29)
1%2F%281%2A2%29%2B1%2F%282%2A3%29%2B1%2F%283%2A4%29+...1%2F%28n%28n%2B1%29%29=highlight%281-1%2F%28n%2B1%29%29