$111 \frac{1}{2}+111 \frac{1}{6}+111 \frac{1}{12}+111 \frac{1}{20}+111 \frac{1}{30} ?$ का मूल्य क्या है

अभिव्यक्ति

$=111+\frac{1}{2}+111+\frac{1}{6}+111+\frac{1}{12}+111+\frac{1}{20}+$

$111+\frac{1}{30}=5 \times 111+\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\right)$

$=555+\left(\frac{1}{1 \times 2}+\frac{1}{2 \times 3}+\frac{1}{3 \times 4}+\frac{1}{4 \times 5}+\frac{1}{5 \times 6}\right)=555+$

$\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\right)$

$=555+\left(1-\frac{1}{6}\right)=555 \frac{5}{6}$