The value of frac{1}{1 cdot 2 cdot 3} + frac{ | vedclass

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Question

(A) The given expression is $S = \frac{1}{1 \cdot 2 \cdot 3} + \frac{1}{2 \cdot 3 \cdot 4} + \frac{1}{3 \cdot 4 \cdot 5} + \frac{1}{4 \cdot 5 \cdot 6}

Vedclass · Accepted Answer

$\frac{7}{30}$

Vedclass · Answer

(A) The given expression is $S = \frac{1}{1 \cdot 2 \cdot 3} + \frac{1}{2 \cdot 3 \cdot 4} + \frac{1}{3 \cdot 4 \cdot 5} + \frac{1}{4 \cdot 5 \cdot 6}$.Calculating each term individually:$\frac{1}{6} + \frac{1}{24} + \frac{1}{60} + \frac{1}{120}$.To add these fractions,find the least common multiple $(LCM)$ of $6, 24, 60, 120$,which is $120$.$S = \frac{20}{120} + \frac{5}{120} + \frac{2}{120} + \frac{1}{120}$.$S = \frac{20 + 5 + 2 + 1}{120} = \frac{28}{120}$.Simplifying the fraction by dividing both numerator and denominator by $4$,we get $\frac{7}{30}$.

The value of $\frac{1}{1 \cdot 2 \cdot 3} + \frac{1}{2 \cdot 3 \cdot 4} + \frac{1}{3 \cdot 4 \cdot 5} + \frac{1}{4 \cdot 5 \cdot 6}$ is:

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