Question

A = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42

Answer 1

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

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

A=1-1/7

A=6/7

Answer 2

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

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

A = 1/1 - 1/7 

A = 6/7

Answer 3

 

1/2+1/6+1/12+1/20+1/30+1/42 
= 1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7 
=(1-1/2)+(1/2-1/3)+....+(1/6-1/7) 
=1-1/2+1/2-1/3+....+1/6-1/7 
=1-1/7=6/7

Answer 4

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)

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

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

\(=\frac{1}{1}-\frac{1}{7}=\frac{6}{7}\)