Question

Tính: \(\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)

Answer 1

Ta có:\(\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)

       =\(\frac{5}{3}\times\left(\frac{3}{28}+\frac{3}{70}+\frac{3}{130}+...+\frac{3}{700}\right)\)  

      =\(\frac{5}{3}\times\left(\frac{3}{4\times7}+\frac{3}{7\times10}+\frac{3}{10\times13}+...+\frac{3}{25\times28}\right)\)  

      =\(\frac{5}{3}\times\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{25}-\frac{1}{28}\right)\)

      =\(\frac{5}{3}\times\left(\frac{1}{4}-\frac{1}{28}\right)\)

      =\(\frac{5}{3}\times\frac{3}{14}\)

      =\(\frac{5}{14}\)

Ko bít có đúng ko nhưng cứ thử nhé