a=1,b=3,ab分之一+(a+2)(b+2)+(a+4)(b+4)+(a+6)(b+6)+…………+(a+100)(b+100)

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/25 03:28:56
a=1,b=3,ab分之一+(a+2)(b+2)+(a+4)(b+4)+(a+6)(b+6)+…………+(a+100)(b+100)a=1,b=3,ab分之一+(a+2)(b+2)+(a+4)(b+4

a=1,b=3,ab分之一+(a+2)(b+2)+(a+4)(b+4)+(a+6)(b+6)+…………+(a+100)(b+100)
a=1,b=3,ab分之一+(a+2)(b+2)+(a+4)(b+4)+(a+6)(b+6)+…………+(a+100)(b+100)

a=1,b=3,ab分之一+(a+2)(b+2)+(a+4)(b+4)+(a+6)(b+6)+…………+(a+100)(b+100)
答:a=1,b=3
1/(ab)+1/[(a+2)(b+2)]+1/[(a+4)(b+4)]+1/[(a+6)(b+6)]+.+1/[(a+100)(b+100)]
=1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9)+.+1/(101×103)
=(1/2)[2/(1×3)+2/(3×5)+2/(5×7)+2/(7×9)+.+2/(101×103)]
=(1/2)(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+...+1/101-1/103)
=(1/2)(1-1/103)
=(1/2)(102/103)
=51/103