If $$f(x) = \frac{1}{x}-\frac{1}{x+1}$$,then what is the value of $$f(1) + f(2) + f(3) + ......f(10)?$$

$$f(x)=\frac{1}{x}-\frac{1}{x+1}$$

So, $$f(1)=\frac{1}{1}-\frac{1}{2}\ .$$

$$f(2)=\frac{1}{2}-\frac{1}{3}\ .$$

$$f(3)=\frac{1}{3}-\frac{1}{4}\ .$$

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.$$f(10)=\frac{1}{10}-\frac{1}{11}\ .$$

So, $$f\left(1\right)+f\left(2\right)+....+f(10)=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.....-\frac{1}{11}.$$

or, $$f\left(1\right)+f\left(2\right)+....+f(10)=\frac{1}{1}-\frac{1}{11}=\frac{10}{11}.$$

B is correct choice.