Tính nhanh: 4/1x3x5 4/3x5x7 4/5x7x9 4/7x9x11 4/9x11x13
Giải thích
\[\frac{4}{{1 \times 3 \times 5}} + \frac{4}{{3 \times 5 \times 7}} + ... + \frac{4}{{9 \times 11 \times 13}}\]
\[ = \frac{1}{{1 \times 3}} - \frac{1}{{3 \times 5}} + \frac{1}{{3 \times 5}} - \frac{1}{{5 \times 7}} + ... + \frac{1}{{9 \times 11}} - \frac{1}{{11 \times 13}}\]
\[ = \frac{1}{{1 \times 3}} - \frac{1}{{11 \times 13}}\]
\( = \frac{1}{1} - \frac{1}{3} - \left( {\frac{1}{{11}} - \frac{1}{{13}}} \right)\)
\[ = \frac{{140}}{{429}}\].