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\(\frac{11}{2}\): \(\frac{11}{3}\): \(\frac{11}{4}\)
= \(\frac{11}{2}\): ( \(\frac{3}{11}\): \(\frac{4}{11}\)
\(\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5}\right):\left(\frac{1}{4}-\frac{1}{6}\right)\)
\(=\left(\frac{1}{2.3}+\frac{1}{4.5}\right):\frac{2}{4.6}\)
\(=\left(\frac{1}{6}+\frac{1}{20}\right).2.6\)
\(=\frac{13}{60}.2.6=\frac{13}{5}\)
a)\(\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right)=\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}=\frac{3.4.5}{2.3.4}=\frac{5}{2}\)
b)\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}=\frac{1.2.3}{2.3.4}=\frac{1}{4}\)
\(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}\)
\(=1-\frac{1}{4}=\frac{3}{4}\)
= 1/1 -(1/2-1/2) -(1/3-1/3)-1/4
=1-1/4=3/4