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Question Number 68589 by peter frank last updated on 13/Sep/19

Answered by $@ty@m123 last updated on 14/Sep/19

$$\underset{k=2}{\sum ^n}\frac{1}{n(n+1)}$$$$=\underset{k=2}{\sum ^n}(\frac{1}{n}-\frac{1}{n+1})$$$$=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{n-1}-\frac{1}{n}+\frac{1}{n}-\frac{1}{n+1}$$$$=\frac{1}{2}-\frac{1}{n+1}$$$$=\frac{n-1}{2(n+1)}$$

Commented by peter frank last updated on 14/Sep/19

$$thankyou$$

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