Question

Tính tổng 1 cách hợp lý

A=6/4.7+6/7.10+6/10.13+...+6/73.76

 

Answer 1

A=6/4.7+6/7.10+6/10.13+...+6/73.76

\(=2.\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{73.76}\right)\)

\(=2.\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{73}-\frac{1}{76}\right)\)

\(=2.\left(\frac{1}{4}-\frac{1}{76}\right)=2.\frac{9}{38}=\frac{9}{19}\) 

Answer 2

A=6/4.7+6/7.10 +...+6/73.76=6/4-6/7+6/7-6/10+...+6/73-6/76=6/4-6/76=27/19

Answer 3

\(A=\frac{6}{4.7}+\frac{6}{7.10}+\frac{6}{10.13}+...+\frac{6}{73.76}\)

\(\frac{1}{2}A=\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{73.76}\)

\(\frac{1}{2}A=\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{73}-\frac{1}{76}\)

\(\frac{1}{2}A=\frac{1}{4}-\frac{1}{76}=\frac{9}{38}\)

\(\Rightarrow A=\frac{9}{38}:\frac{1}{2}=\frac{9}{19}\)