已知数列{an}满足a1=1,2a(n+1)an+3a(n+1)+an+2=0.(1) 求证{1/an+1}是等差数列;(2)求通项公式an.怎么打下标呀 a(n+1)就是第n+1项难题呀 求破求破
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![已知数列{an}满足a1=1,2a(n+1)an+3a(n+1)+an+2=0.(1) 求证{1/an+1}是等差数列;(2)求通项公式an.怎么打下标呀 a(n+1)就是第n+1项难题呀 求破求破](/uploads/image/z/1072062-54-2.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7Ban%7D%E6%BB%A1%E8%B6%B3a1%3D1%2C2a%EF%BC%88n%2B1%29an%2B3a%28n%2B1%29%2Ban%2B2%3D0.%281%29+%E6%B1%82%E8%AF%81%7B1%2Fan%2B1%7D%E6%98%AF%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%EF%BC%9B%EF%BC%882%EF%BC%89%E6%B1%82%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8Fan.%E6%80%8E%E4%B9%88%E6%89%93%E4%B8%8B%E6%A0%87%E5%91%80+a%EF%BC%88n%2B1%EF%BC%89%E5%B0%B1%E6%98%AF%E7%AC%ACn%2B1%E9%A1%B9%E9%9A%BE%E9%A2%98%E5%91%80+%E6%B1%82%E7%A0%B4%E6%B1%82%E7%A0%B4)
已知数列{an}满足a1=1,2a(n+1)an+3a(n+1)+an+2=0.(1) 求证{1/an+1}是等差数列;(2)求通项公式an.怎么打下标呀 a(n+1)就是第n+1项难题呀 求破求破
已知数列{an}满足a1=1,2a(n+1)an+3a(n+1)+an+2=0.
(1) 求证{1/an+1}是等差数列;
(2)求通项公式an.
怎么打下标呀 a(n+1)就是第n+1项
难题呀 求破求破
已知数列{an}满足a1=1,2a(n+1)an+3a(n+1)+an+2=0.(1) 求证{1/an+1}是等差数列;(2)求通项公式an.怎么打下标呀 a(n+1)就是第n+1项难题呀 求破求破
这个题目一看就该两边同除以a(n+1)*an 达到需要的变形式.但是再看发现有一个常数项,直接除是变不成功的,所以考虑除{[a(n+1)+N]*(an+N )}如果做题目灵活可以猜得出这里的N=1,不猜要通过凑式子来得到.但直接除还是不行,我们把式子加加减减变形为:2a(n+1)an+2a(n+1)+2an+2=an+1-a(n+1)-1左边因式分2{[a(n+1)+1]*(an+1 )}=(an+1)-[a(n+1)+1]然后两边同除{[a(n+1)+1]*(an+1)}得到{1/[a(n+1)+1]}-[1/(an+1)]=-2
到这里我就不多说了.另外二楼的过程纯粹猜题瞎扯
可设x=a(n+1),y=an.===>2xy+3x+y+2=0.(变形)===>[1/(x+1)]-[1/(y+1)]=2.===>{1/[a(n+1)+1]}-{1/[an+1]}=2.===>{1/(an+1)}是首项为1/2,公差为2的等差数列。===>1/(an+1)=(1/2)+2(n-1).===>an=(5-4n)/(4n-3).(n=1,2,3,...)
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