TÍNH 1+1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55+1/66

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1. Đáp án:

    11/6

   Giải thích các bước giải:

    1+1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45+1/55+1/66

   =2/2+2/6+2/12+2/20+……….+2/90+2/110+2/132

   =2x(1/1×2+1/2×3+1/3×4+1/4×5+……..+1/10×11+1/11×12)

   =2x(1-1/2+1/2-1/3+1/3-1/4+…………+1/10-1/11+1/11-1/12)

   =2x(1-1/12)

   =2×11/12

   =11/6

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2. Đáp án:

    \(\frac{11}{6}\)

   Giải thích các bước giải:

   \[\begin{array}{l}
   1 + \frac{1}{3} + \frac{1}{6} + \frac{1}{{10}} + \frac{1}{{15}} + \frac{1}{{21}} + \frac{1}{{28}} + \frac{1}{{36}} + \frac{1}{{45}} + \frac{1}{{55}} + \frac{1}{{66}}\\
    = \frac{2}{2} + \frac{2}{6} + \frac{2}{{12}} + \frac{2}{{20}} + \frac{2}{{30}} + …+ \frac{2}{{90}} + \frac{2}{{110}} + \frac{2}{{132}}\\
    = 2 \times \left( {\frac{1}{{1 \times 2}} + \frac{1}{{2 \times 3}} + \frac{1}{{3 \times 4}} + \frac{1}{{4 \times 5}} + \frac{1}{{5 \times 6}} + …+ \frac{1}{{9 \times 10}} + \frac{1}{{10 \times 11}} + \frac{1}{{11 \times 12}}} \right)\\
    = 2 \times \left( {1 – \frac{1}{2} + \frac{1}{2} – \frac{1}{3} + \frac{1}{3} – \frac{1}{4} + \frac{1}{4} – \frac{1}{5} +… + \frac{1}{{10}} – \frac{1}{{11}} + \frac{1}{{11}} – \frac{1}{{12}}} \right)\\
    = 2 \times \left( {1 – \frac{1}{{12}}} \right)\\
    = 2 \times \frac{{11}}{{12}}\\
    = \frac{{11}}{6}
   \end{array}\]

    

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