六年级数学1/6+1/12+1/20+1/30+1/42+1/56

题目

六年级数学1/6+1/12+1/20+1/30+1/42+1/56
①1/6+1/12+1/20+1/30+1/42+1/56
②2/3×5+2/5×7+2/7×9.2/49×51+2/51×53
谢谢

答案

①1/6+1/12+1/20+1/30+1/42+1/56
=(3-2)/6+(4-3)/12+(5-4)/20+(6-5)/30+(7-6)/42+(8-7)/56
=1/2-1/3+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)
=1/2-1/8
=3/8
②2/3×5+2/5×7+2/7×9.2/49×51+2/51×53
=(5-3)/3×5+(7-5)/5×7+(9-7)/7×9……(51-49)/49×51+(53-51)/51×53
=1/3-1/5+(1/5-1/7)+(1/7-1/9)……(1/49-1/51)+(1/51-1/53)
=1/3-1/53
=50/159
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