数列{an},an=1/[n*2^(n-1)].前N项和为Sn,求证Sn
来源:学生作业帮助网 编辑:六六作业网 时间:2025/02/08 03:39:51
数列{an},an=1/[n*2^(n-1)].前N项和为Sn,求证Sn数列{an},an=1/[n*2^(n-1)].前N项和为Sn,求证Sn数列{an},an=1/[n*2^(n-1)].前N项和
数列{an},an=1/[n*2^(n-1)].前N项和为Sn,求证Sn
数列{an},an=1/[n*2^(n-1)].前N项和为Sn,求证Sn
数列{an},an=1/[n*2^(n-1)].前N项和为Sn,求证Sn
证明:
∵当n>1时,(n-2)2^(n-1)≥0
∴n2^(n-1)-2^n≥0
n2^(n-1)≥2^n
即:1/[n2^(n-1)]≤1/2^n
∵数列{a[n]},a[n]=1/[n2^(n-1)],前n项和为S[n]
∴S[n]
=1+1/(2*2^1)+...+1/[n2^(n-1)]
≤1+1/2^2+...+1/2^n
=1+(1/4)[1-1/2^(n-1)]/(1-1/2)
=1+(1/2)[1-1/2^(n-1)]
<1+1/2
=3/2
用放缩法或者先求得Sn的表达式..........
An=1/n^2 数列求和An=1/n^2 数列(An)求和
数列{an}满足a1=1 an+1=2n+1an/an+2n
数列{an},a1=1,an+1=2an-n^2+3n,求{an}.
数列{an}中,a1=1,an+1/an=n/n+2,求an
设数列{an}中,若an+1 =an+ an+2 (n∈N*),则称数列{an}为“凸数列” .设数列{an}为“凸数列”求第二问证明设数列{an}中,若an+1 =an+ an+2 (n∈N*),则称数列{an}为“凸数列” .设数列{an}为“凸数列”,若a1 =1,
数列{an}中,an=-2n+2*(-1)^n,则数列{an}的前n项和sn为
已知数列an中,a1=1,an/an-1=n+1/n,n大于等于2,求an
数列{an}满足a1=2,a(n+1)=2an+n+2,求an
数列an满足a1=1/3,Sn=n(2n-1)an,求an
数列{an}中,a1=2,an+1=an+ln(n+1/n),求通项公式
数列{an},a1=3,an*a(n+1)=(1/2)^n,求an
数列an,a1=1.an+1/an=n+2/n,求通项公式,
已知数列{an}中,a(n+1)=an+2^n,a1=3,求an
数列an中,若a( n+1)=an+(2n-1)求an
数列an集合中,a1=2,an+1=an+(2n+1),求an.
设数列{an}中,a1=2,an+1=an+n+1,则通项an=?
数列{an}中,a1=35,an+1-an=2n-1,求an
已知数列an,a1=1 an+1-an=2的n次幂求an