Question

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1/ 2 x 3 + 1 / 3 x 4 + ..... + 1 / x . [x + 1]

 

Answer 1

\(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x.\left(x+1\right)}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}\)

\(=\frac{1}{2}-\frac{1}{x+1}\)

\(=\frac{x+1}{2.\left(x+1\right)}-\frac{2}{2.\left(x+1\right)}=\frac{\left(x+1\right)-2}{2.\left(x+1\right)}\)