\(A=\dfrac{1}{2}+\dfrac{5}{6}+\dfrac{11}{12}+\dfrac{29}{30}+\dfrac{41}{42}+\dfrac{55}{56}\\ =\left(1-\dfrac{1}{2}\right)+\left(1-\dfrac{1}{6}\right)+\left(1-\dfrac{1}{12}\right)+\left(1-\dfrac{1}{30}\right)+\left(1-\dfrac{1}{42}\right)+\left(1-\dfrac{1}{56}\right)\\ =6-\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}\right)\\ =6-\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{5\cdot6}+\dfrac{1}{6\cdot7}+\dfrac{1}{7\cdot8}\right)\\ 6-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}\right)\\ =6-\left(1-\dfrac{1}{4}+\dfrac{1}{5}-\dfrac{1}{8}\right)=\dfrac{207}{40}\)
Chắc đề thiếu, nhưng mình cứ làm hướng kiểu kia trước nhaa
Giải:
1/2+ 5/6+ 11/12+ 29/30+ 41/42+ 55/56
=(1- 1/2)+ (1-1/6)+ (1- 1/12)+ (1-1/30)+ (1- 1/42)+ (1- 1/56)
=1- 1/2+ 1- 1/6+1-1/12 1-1/30+1-1/42+1-1/56
=6-(1/2+1/6+1-1/12+1/30+1/42+1/56)
=6-(1/1.2+1/2.3+1/3.4+1/5.6+1/6.7+1/7.8)
=6-(1/1-1/2+1/2-1/3+1/3-1/4+1/5-1/6+1/6-1/7+1/7-1/8)
=6-(1/1-1/4+1/5-1/8)
=6-33/40
=207/40
Chúc bạn học tốt!
\(\dfrac{1}{2}+\dfrac{5}{6}+\dfrac{11}{12}+\dfrac{29}{30}+\dfrac{41}{42}+\dfrac{55}{56}\)
\(=\left(1-\dfrac{1}{2}\right)+\left(1-\dfrac{5}{6}\right)+\left(1-\dfrac{11}{12}\right)+\left(1-\dfrac{29}{30}\right)+\left(1-\dfrac{41}{42}\right)\left(1-\dfrac{55}{56}\right)\)
\(=6-\left(\dfrac{1}{1.2}+\dfrac{5}{2.3}+\dfrac{11}{3.4}+\dfrac{29}{5.6}+\dfrac{41}{6.7}+\dfrac{55}{7.8}\right)\)
\(=6-\left(1-\dfrac{1}{4}+\dfrac{1}{5}-\dfrac{1}{8}\right)=\dfrac{207}{40}\)
