数列an满足a1=2,an+1(n+1为下标)-=2n+1n+1为上标)*an/(n+1/2)an+2的n次方

来源：学生作业帮编辑：拍题作业网作业帮分类：数学作业时间：2024/04/30 18:13:48

数列an满足a1=2,an+1(n+1为下标)-=2n+1n+1为上标)*an/(n+1/2)an+2的n次方
（1）设bn=2的n次方除以an,求数列{bn}的通项公式
（2）设cn=1/n（n+1）an+1（n+1为下标）

你问的是不是这样?
a(n+1)=2^(n+1)an/[(n+1/2)an+2^n]
(1)易得2^(n+1)/a(n+1)=[(n+1/2)an+2^n]/an=n+1/2+2^n/an
即b(n+1)=bn+n+1/2
bn=b(n-1)+(n-1)+1/2
=b1+1+2+……+(n-1)+1/2(n-1)=1+1/2[n(n-1)]+1/2(n-1)=1/2(n^2+1)
(2)an=2^n/bn=2^(n+1)/(n^2+1)
cn=(n^2+2n+2)/[2^(n+2)(n^2+n)]=(n+1)/[2^(n+1)n]-(n+2)/[2^(n+2)(n+1)]
前n项和为Sn=(2/4*1-3/8*2)+(3/8*2-4/16*3)+……+{(n+1)/[2^(n+1)n]-(n+2)/[2^(n+2)(n+1)]}
=2/4*1-(n+2)/[2^(n+2)(n+1)]（裂项相消法）
=1/2-(n+2)/[2^(n+2)(n+1)]

数列{an},a1=2,an+1(下标)=an下标+n+1 求通项an下标设数列{an}的前n项和为Sn,已知Sn=2an-2n+1,（n为下标,n+1为上标）,求通项公式? 数列{an}满足a1=1 an+1=2n+1an/an+2n 已知数列{AN}满足A1=1,AN+1=2AN+2的N次方. 数列{an}满足a1=33,a(n+1)-an=2n,则an/n的最小值为_ 设数列{an}满足a1=2 an+1-an=3×（2的2n-1次方）【n为下脚标、n+1也是下脚标】已知数列｛an｝满足a1=1,an=3的n-1次方+an-1（n≥2）在数列{an}中,a1=2,a（n+1）- an = 2的n次方,求通项an n+1在下标. 设数列｛an｝满足an+1/an=n+2/n+1,且a1＝2 已知数列an满足a1=1,an-2a下标(n-1)-2*(n-1)=0,(n∈N*,n≥2) 已知数列{an}中,a1=1,满足an+1=an+2n,n属于N*,则an等于已知数列满足：A1=1.AN+1=1/2AN+N,N奇数,AN-2N.N偶数