(0,5 điểm) Thực hiện phép tính D = 5 2 1.6 + 5 2 6.11 + 5 2 11.16 + . . . + 5 2 26.31 .

Hướng dẫn giải

Ta có: \(D = \frac{{{5^2}}}{{1.6}} + \frac{{{5^2}}}{{6.11}} + \frac{{{5^2}}}{{11.16}} + ... + \frac{{{5^2}}}{{26.31}}\)

\(D = 5\left( {\frac{5}{{1.6}} + \frac{5}{{6.11}} + \frac{5}{{11.16}} + ... + \frac{5}{{26.31}}} \right)\)

\(D = 5\left( {\frac{1}{1} - \frac{1}{6} + \frac{1}{6} - \frac{1}{{11}} + \frac{1}{{11}} - \frac{1}{{16}} + ... + \frac{1}{{26}} - \frac{1}{{31}}} \right)\)

\(D = 5\left( {\frac{1}{1} - \frac{1}{{31}}} \right)\)

\(D = 5.\frac{{30}}{{31}}\)

\(D = \frac{{150}}{{31}}\).