Tính tổng biểu thức 6/8 + 6/56 + 6/140 + ... + 6/1100 + 6/1400
Giải thích
Ta có: \[\frac{6}{8} + \frac{6}{{56}} + \frac{6}{{140}} + ... + \frac{6}{{1100}} + \frac{6}{{1400}}\]
\[ = \frac{{2.3}}{{2.4}} + \frac{{2.3}}{{2.28}} + \frac{{2.3}}{{2.70}} + ... + \frac{{2.3}}{{2.550}} + \frac{{2.3}}{{2.700}}\]
\[ = \frac{3}{4} + \frac{3}{{28}} + \frac{3}{{70}} + ... + \frac{3}{{550}} + \frac{3}{{700}}\]
\[ = \frac{3}{{1.4}} + \frac{3}{{4.7}} + \frac{3}{{7.10}} + ... + \frac{3}{{22.25}} + \frac{3}{{25.28}}\]
\[ = 1 - \frac{1}{4} + \frac{1}{4} - \frac{1}{7} + \frac{1}{7} - \frac{1}{{10}} + ... + \frac{1}{{22}} - \frac{1}{{25}} + \frac{1}{{25}} - \frac{1}{{28}}\]
\[ = 1 - \frac{1}{{28}}\]\[ = \frac{{28}}{{28}} - \frac{1}{{28}} = \frac{{27}}{{28}}\].