Question 9

The sum of $$n-$$ terms of sequence $$\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}.......$$ is

Solution

$$\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}.......$$

$$\dfrac{2-1}{1\times2}+\dfrac{3-2}{2\times3}+\dfrac{4-3}{3\times4}+....$$

$$\left(\dfrac{1}{1}-\dfrac{1}{2}\right)+\left(\dfrac{1}{2}-\dfrac{1}{3}\right)+\left(\dfrac{1}{3}-\dfrac{1}{4}\right)+....+\left(\dfrac{1}{n}-\dfrac{1}{n+1}\right)$$

$$1-\dfrac{1}{n+1}$$

$$\dfrac{n}{n+1}$$

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