SOLUTION: If An=1/n(n+1) for all positive integer n, What is the sum of the first 100 elements of An?

Question 1057149: If An=1/n(n+1) for all positive integer n, What is the sum of the first 100 elements of An?
Answer by ikleyn(52847) (Show Source): You can put this solution on YOUR website!
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If An=1/n(n+1) for all positive integer n, What is the sum of the first 100 elements of An?
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 = .   (1)


Each term  is the difference of two terms


 = .


If you replace each term in the sum (1) by the correcsponding difference and cancel all adjacent terms with opposite signs, you will get


 = 1 - .


At n = 100,   = .

Answer.   = .

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