Question

用简便方法计算4/3-7/12+9/20-11/30+13/42-15/56+17/72-19/9

用简便方法计算4/3-7/12+9/20-11/30+13/42-15/56+17/72-19/90

Answer 1

解;4/3-7/12+9/20-11/30+13/42-15/56+17/72-19/90
=4/3-(3+4)/(3*4)+(4+5)/(4*5)
-(5+6)/(5*6)+(6+7)/(6*7)
-(7+8)/(7*8)+(8+9)/(8*9)
-(9+10)/(9*10)
=4/3-(1/3+1/4)+(1/4+1/5)-(1/5+1/6)
+(1/6+1/7)-(1/7+1/8)+(1/8+1/9)
-(1/9+1/10)
=4/3-1/3-1/4+1/4+1/5-1/5-1/6+1/6+1/7-1/7
-1/8+1/8+1/8-1/9-1/10
=1-1/10
=9/10
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