Find the sum of the series: frac{1}{1 times 2 | vedclass

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(B) The general term of the series is $T_k = \frac{1}{k(k + 1)}$.Using partial fractions,we can write $T_k = \frac{1}{k} - \frac{1}{k + 1}$.The sum $S

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$\frac{n}{n + 1}$

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(B) The general term of the series is $T_k = \frac{1}{k(k + 1)}$.Using partial fractions,we can write $T_k = \frac{1}{k} - \frac{1}{k + 1}$.The sum $S_n$ is given by $\sum_{k=1}^{n} (\frac{1}{k} - \frac{1}{k + 1})$.Expanding the sum: $S_n = (1 - \frac{1}{2}) + (\frac{1}{2} - \frac{1}{3}) + (\frac{1}{3} - \frac{1}{4}) + \dots + (\frac{1}{n} - \frac{1}{n + 1})$.This is a telescoping series where intermediate terms cancel out.$S_n = 1 - \frac{1}{n + 1} = \frac{n + 1 - 1}{n + 1} = \frac{n}{n + 1}$.

Find the sum of the series: $\frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \frac{1}{3 \times 4} + \dots + \frac{1}{n(n + 1)}$

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