What is the following sum?

(1/1*2) + (1/2*3) + (1/3*4) + . . . + (1/(n-1)n)

Experiment, Conjucture the value, and then prove by induciton

/ means division, ex. 1/2=.5

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- September 12th 2010, 11:10 PMtaylor1234Induction Method
What is the following sum?

(1/1*2) + (1/2*3) + (1/3*4) + . . . + (1/(n-1)n)

Experiment, Conjucture the value, and then prove by induciton

/ means division, ex. 1/2=.5 - September 13th 2010, 12:00 AMProve It
I assume that this is

.

Notice that you can write the term as

.

So that means we can rewrite the sum as

, since all but the first and last term cancel.