Question

cho B= 1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7

Rút gọn biểu thức bằng phương pháp gọn nhất

Answer 1

B = 1/1.2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7

B = 1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7

B = 1 - 1/7

B = 6/7 

Answer 2

\(B=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)

\(=1-\frac{1}{7}\)

\(=\frac{6}{7}\)