设数列{an}满足Sn=n^2+1,Pn=1/a1.a2+1/a2.a3+.+1/an.an+1,求n=?
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/07/13 21:50:17
设数列{an}满足Sn=n^2+1,Pn=1/a1.a2+1/a2.a3+.+1/an.an+1,求n=?
Sn=n^2+1 S(n-1)=(n-1)^2+1
an=Sn-S(n-1)=2n-1
1/an*a(n+1)=1/(2n-1)(2n+1)=(1/2)[1/(2n-1)-1/(2n+1)]
Pn=1/1*3+1/3*5+...+1/(2n-1)(2n+1)
=(1/2)(1-1/3)+(1/2)(1/3-1/5)+(1/2)[1/(2n-1)-1/(2n+1)]
=(1/2)[1-1/(2n+1)]
=n/(2n+1)
an=Sn-S(n-1)=2n-1
1/an*a(n+1)=1/(2n-1)(2n+1)=(1/2)[1/(2n-1)-1/(2n+1)]
Pn=1/1*3+1/3*5+...+1/(2n-1)(2n+1)
=(1/2)(1-1/3)+(1/2)(1/3-1/5)+(1/2)[1/(2n-1)-1/(2n+1)]
=(1/2)[1-1/(2n+1)]
=n/(2n+1)
设数列{an}满足Sn=n^2+1,Pn=1/a1.a2+1/a2.a3+.+1/an.an+1,求n=?
已知数列{an}前n项和Sn=n^2,记Pn=1/(a1*a2)+1/(a2*a3)+...+1/(an*an+1),求
设数列{an}的前n项和为Sn,并且满足2Sn=an²+n,an>0.(1)求a1,a2,a3.(2)猜想{a
已知数列{an}满足a1+a2+a3+...+an=n^2+2n.(1)求a1,a2,a3,a4
设数列{an}满足a1+2a2+3a3+.+nan=n(n+1)(n+2)
设an=根号n+根号(n+1),求Sn=a1+a2+a3+...+an
数列an满足sn=3an-1/2 计算a1,a2,a3,a4 猜an通项 求an前n项和sn
设数列an满足a1+3a2+3^2a3+.+3^n-1an=n/3,n∈N*,求数列an的通项公式
在各项为正的数列{an}中,数列的前n项和Sn满足Sn=2分之一(an+an分之一),(1)求a1,a2,a3.
设数列{an}的前n项和为Sn,满足2Sn=an+1-2^n+1+1,且a1,a2+5.a3成等差数列
设数列{an}的前n项和为Sn,满足2Sn=an+1-2^n+1+1,且a1,a2+5.a3成等差数
设数列an的前n项和为Sn,满足2Sn=an-2∧n+1 +1 ,且a1,a2+5,a3成等差