数列an是首次为1的正数列,且(an+1)²/n - an²/n+1 + (an+1*an)/(n+1)n =0,求通项公式数列an是首次为1的正数列,且(an+1)²/n - an²/(n+1) + (an+1*an)/(n+1)n =0,求通项公式
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/19 05:29:04
![数列an是首次为1的正数列,且(an+1)²/n - an²/n+1 + (an+1*an)/(n+1)n =0,求通项公式数列an是首次为1的正数列,且(an+1)²/n - an²/(n+1) + (an+1*an)/(n+1)n =0,求通项公式](/uploads/image/z/129070-46-0.jpg?t=%E6%95%B0%E5%88%97an%E6%98%AF%E9%A6%96%E6%AC%A1%E4%B8%BA1%E7%9A%84%E6%AD%A3%E6%95%B0%E5%88%97%2C%E4%B8%94%28an%2B1%29%26%23178%3B%2Fn+-+an%26%23178%3B%2Fn%2B1+%2B+%28an%2B1%2Aan%29%2F%28n%2B1%29n+%3D0%2C%E6%B1%82%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%E6%95%B0%E5%88%97an%E6%98%AF%E9%A6%96%E6%AC%A1%E4%B8%BA1%E7%9A%84%E6%AD%A3%E6%95%B0%E5%88%97%2C%E4%B8%94%28an%2B1%29%26%23178%3B%2Fn+-+an%26%23178%3B%2F%28n%2B1%29+%2B+%28an%2B1%2Aan%29%2F%28n%2B1%29n+%3D0%2C%E6%B1%82%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F)
数列an是首次为1的正数列,且(an+1)²/n - an²/n+1 + (an+1*an)/(n+1)n =0,求通项公式数列an是首次为1的正数列,且(an+1)²/n - an²/(n+1) + (an+1*an)/(n+1)n =0,求通项公式
数列an是首次为1的正数列,且(an+1)²/n - an²/n+1 + (an+1*an)/(n+1)n =0,求通项公式
数列an是首次为1的正数列,且(an+1)²/n - an²/(n+1) + (an+1*an)/(n+1)n =0,求通项公式
数列an是首次为1的正数列,且(an+1)²/n - an²/n+1 + (an+1*an)/(n+1)n =0,求通项公式数列an是首次为1的正数列,且(an+1)²/n - an²/(n+1) + (an+1*an)/(n+1)n =0,求通项公式
(an+1)²/n - an²/(n+1) + (an+1*an)/(n+1)n =0,
(n+1)(an+1)² + (an+1*an)- nan² =0,
[(n+1)a(n+1)-nan]*[a(n+1)+an]=0
a(n+1)+an>0
(n+1)a(n+1)-nan=0
则{nan}是等差数列,公差为0,即为常数列
首项为1
nan=1
an=1/n
(an+1)²/n - an²/(n+1) + (an+1*an)/(n+1)n =0
方程两边乘以(n+1)n得
(n+1)(an+1)²+an+1*an-nan²=0
[(n+1)an+1-nan](an+1+an)=0
n+1an+1=nan或an+1=-an
an是首项为1的正数列
an+1=-an舍去...
全部展开
(an+1)²/n - an²/(n+1) + (an+1*an)/(n+1)n =0
方程两边乘以(n+1)n得
(n+1)(an+1)²+an+1*an-nan²=0
[(n+1)an+1-nan](an+1+an)=0
n+1an+1=nan或an+1=-an
an是首项为1的正数列
an+1=-an舍去
n+1an+1/nan=1
nan/n-1an-1
……
2a2/1a1=1
相乘得nan/1a1=1
nan=1
an=1/n
收起