早教吧作业答案频道 -->数学-->
已知数列bn=2n+1,求(1/b1b2)+(1/b2b3)+(1/b3b4)+…+（1/bnbn+1）
题目详情
已知数列bn=2n+1,求(1/b1b2)+(1/b2b3)+(1/b3b4)+…+（1/bnbn+1）
▼优质解答
答案和解析
bn=2n+1 b(n+1)=2n+3
1/bnb(n+1)=1/(2n+1)(2n+3)
=(1/2)[(2n+3)-(2n+1)]/[(2n+1)(2n+3)]
=(1/2)[1/(2n+1)-1/(2n+3)]
则(1/b1b2)+(1/b2b3)+(1/b3b4)+…+（1/bnbn+1）
=(1/2)*(1/3-1/5)+(1/2)*(1/5-1/7)+(1/2)*(1/7-1/9)+...+(1/2)*[1/(2n+1)-1/(2n+3)]
=(1/2)*[1/3-1/(2n+3)]
=(1/2)(2n+3-3)/[3(2n+3)]
=n/(6n+9)
希望能帮到你O(∩_∩)O
1/bnb(n+1)=1/(2n+1)(2n+3)
=(1/2)[(2n+3)-(2n+1)]/[(2n+1)(2n+3)]
=(1/2)[1/(2n+1)-1/(2n+3)]
则(1/b1b2)+(1/b2b3)+(1/b3b4)+…+（1/bnbn+1）
=(1/2)*(1/3-1/5)+(1/2)*(1/5-1/7)+(1/2)*(1/7-1/9)+...+(1/2)*[1/(2n+1)-1/(2n+3)]
=(1/2)*[1/3-1/(2n+3)]
=(1/2)(2n+3-3)/[3(2n+3)]
=n/(6n+9)
希望能帮到你O(∩_∩)O
看了 已知数列bn=2n+1,求(...的网友还看了以下：