Lời giải
Ta có \(C = \left( {\frac{{171717}}{{151515}} + \frac{{171717}}{{353535}} + \frac{{171717}}{{636363}} + \frac{{171717}}{{999999}}} \right):\frac{8}{{11}}\)
\( = \left( {\frac{{17.10101}}{{15.10101}} + \frac{{17.10101}}{{35.10101}} + \frac{{17.10101}}{{63.10101}} + \frac{{17.10101}}{{99.10101}}} \right):\frac{8}{{11}}\)
\( = \left( {\frac{{17}}{{15}} + \frac{{17}}{{35}} + \frac{{17}}{{63}} + \frac{{17}}{{99}}} \right):\frac{8}{{11}}\)
\( = \left( {\frac{{17.231}}{{3465}} + \frac{{17.99}}{{3465}} + \frac{{17.55}}{{3465}} + \frac{{17.35}}{{3465}}} \right):\frac{8}{{11}}\)
\( = \left( {\frac{{3927}}{{3465}} + \frac{{1683}}{{3465}} + \frac{{935}}{{3465}} + \frac{{595}}{{3465}}} \right):\frac{8}{{11}}\)
\( = \frac{{7140}}{{3465}}.\frac{{11}}{8} = \frac{{68}}{{33}}.\frac{{11}}{8} = \frac{{17}}{3}.\frac{1}{2} = \frac{{17}}{6}\).
Vậy \(C = \frac{{17}}{6}\).