Đáp án:
\[C = \frac{{175}}{{36}}\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
C = \frac{{{5^2}}}{{1.6}} + \frac{{{5^2}}}{{6.11}} + \frac{{{5^2}}}{{11.16}} + .... + \frac{{{5^2}}}{{31.36}}\\
= 5.\left( {\frac{5}{{1.6}} + \frac{5}{{6.11}} + \frac{5}{{11.16}} + .... + \frac{5}{{31.36}}} \right)\\
= 5.\left( {\frac{{6 - 1}}{{1.6}} + \frac{{11 - 6}}{{6.11}} + \frac{{16 - 11}}{{11.16}} + .... + \frac{{36 - 31}}{{31.36}}} \right)\\
= 5.\left( {1 - \frac{1}{6} + \frac{1}{6} - \frac{1}{{11}} + \frac{1}{{11}} - \frac{1}{{16}} + .... + \frac{1}{{31}} - \frac{1}{{36}}} \right)\\
= 5.\left( {1 - \frac{1}{{36}}} \right)\\
= 5.\frac{{35}}{{36}} = \frac{{175}}{{36}}
\end{array}\)
