数列an满足a1=1,an=2an-1/(2+an-1) (n≥2),用数学归纳法求an的通项公式?
来源:学生作业帮助网 编辑:作业帮 时间:2024/11/16 21:56:55
数列an满足a1=1,an=2an-1/(2+an-1) (n≥2),用数学归纳法求an的通项公式?
数列an满足a1=1,an=2an-1/(2+an-1) (n≥2),用数学归纳法求an的通项公式?
数列an满足a1=1,an=2an-1/(2+an-1) (n≥2),用数学归纳法求an的通项公式?
a2=2*1/(1+2)=2/3
类似的a3=1/2
a4=2/5
a5=1/3
注意,1=2/2,1/2=2/4,1/3=2/6
所以猜想an=2/(1+n)
①k=1已经成立
②假设k=n时an=2/(1+n)成立,k=n+1时,an+1=2an/(2+an)=2/(n+2)=2/((n+1)+1)
即对于k=n+1也成立
由一二可得,对任意n,an有通项公式an=2/(1+n)
数列{An}满足a1=1/2,a1+a2+..+an=n方an,求an
数列{an}满足a1=1 an+1=2n+1an/an+2n
数列{an}满足a1=1,且an=an-1+3n-2,求an
数列an满足a1=2,an+1=4an+9,则an=?
已知数列{an}满足an+1=2an+3.5^n,a1=6.求an
数列an满足a1=2,an+1=an²求an
数列an满足a1=2,an+1=an²求an
已知数列{an}满足a1=1 an+1=an/(3an+1) 则球an
已知数列an满足 a1=1/2,an+1=3an/an+3求证1/an为等差数列已知数列an满足 a1=1/2,an+1=3an/an+3求证1/an为等差数列
已知数列an满足a1=1,1/an+1=根号1/an^2+2,an>0,求an
已知数列{an}满足a1=1,a2=3,an+2=3an+1-2an求an
数列{an}满足:a1=1,an>0,an+1^2-an^2=1,那么an
数列{an}满足:a1=1,an>0,an+1^2-an^2=1,那么an
知数列{an}满足a1=-2,an+1(下标)=2+2an/(1-an),则an为?
已知数列{an}满足a1=1,an+1 -an+2an+1•an=0求通项
已知数列{an}满足a1=2,an+1-an=an+1*an,那么a31等于
数列an满足,a1=8且8an+1an-16an+1+2an+5=0
数列an满足an+1=根号(an^2+1)+an,a1=a>0,求an通项公式