奥数题帮忙。小学的

来源:百度知道 编辑:UC知道 时间:2024/09/22 05:27:03
1乘7分之2+7乘13分之2+13乘19分之2+省略号+145乘151分之2=多少?

乘7分之2+7乘13分之2+13乘19分之2+省略号+145乘151分之2
=2×[1/(1×7)+1/(7×13)+1/(13×19)+……+1/(145×151)]
=2×(1-1/7+1/7-1/13+1/13-1/19+……+1/145-1/151)×1/6
=2×(1-1/151)×1/6
=2×150/151×1/6
=50/151

乘7分之2+7乘13分之2+13乘19分之2+省略号+145乘151分之2
=2×[1/(1×7)+1/(7×13)+1/(13×19)+……+1/(145×151)]
=2×(1-1/7+1/7-1/13+1/13-1/19+……+1/145-1/151)×1/6
=2×(1-1/151)×1/6
=2×150/151×1/6
=50/151
1乘7分之2+7乘13分之2+13乘19分之2+省略号+145乘151分之2=一百五十一分之五十

7/2+13/14+19/26+……+151/290=不知道