The value of frac{1}{1 times 2} + frac{1}{2 t | vedclass

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Question

(C) The given expression is $\sum_{n=1}^{9} \frac{1}{n(n+1)}$.We know that $\frac{1}{n(n+1)} = \frac{1}{n} - \frac{1}{n+1}$.Substituting this into the

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$\frac{9}{10}$

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(C) The given expression is $\sum_{n=1}^{9} \frac{1}{n(n+1)}$.We know that $\frac{1}{n(n+1)} = \frac{1}{n} - \frac{1}{n+1}$.Substituting this into the series,we get:$\left(1 - \frac{1}{2}\right) + \left(\frac{1}{2} - \frac{1}{3}\right) + \left(\frac{1}{3} - \frac{1}{4}\right) + \ldots + \left(\frac{1}{9} - \frac{1}{10}\right)$.This is a telescoping series where all intermediate terms cancel out.$= 1 - \frac{1}{10} = \frac{10 - 1}{10} = \frac{9}{10}$.

The value of $\frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \frac{1}{3 \times 4} + \ldots + \frac{1}{9 \times 10}$ is

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