What is the value of 111 frac{1}{2} + 111 fra | vedclass

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(C) The expression is $111 \frac{1}{2} + 111 \frac{1}{6} + 111 \frac{1}{12} + 111 \frac{1}{20} + 111 \frac{1}{30}$.Since there are $5$ terms,we can wr

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$555 \frac{5}{6}$

Vedclass · Answer

(C) The expression is $111 \frac{1}{2} + 111 \frac{1}{6} + 111 \frac{1}{12} + 111 \frac{1}{20} + 111 \frac{1}{30}$.Since there are $5$ terms,we can write this as $(111 	imes 5) + (\frac{1}{2} + \frac{1}{6} + \frac{1}{12} + \frac{1}{20} + \frac{1}{30})$.$111 	imes 5 = 555$.Now,simplify the sum of fractions: $\frac{1}{1 	imes 2} + \frac{1}{2 	imes 3} + \frac{1}{3 	imes 4} + \frac{1}{4 	imes 5} + \frac{1}{5 	imes 6}$.Using the formula $\frac{1}{n(n+1)} = \frac{1}{n} - \frac{1}{n+1}$,we get:$(1 - \frac{1}{2}) + (\frac{1}{2} - \frac{1}{3}) + (\frac{1}{3} - \frac{1}{4}) + (\frac{1}{4} - \frac{1}{5}) + (\frac{1}{5} - \frac{1}{6})$.This simplifies to $1 - \frac{1}{6} = \frac{5}{6}$.Adding the integer part,we get $555 + \frac{5}{6} = 555 \frac{5}{6}$.

What is the value of $111 \frac{1}{2} + 111 \frac{1}{6} + 111 \frac{1}{12} + 111 \frac{1}{20} + 111 \frac{1}{30}$?

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