数列{an}中,a1=1,an+1-2an=(n+2)/n/(n+1),则a2,a3,a4,分别为多少,猜想an=_数学解答

数列{an}中,a1=1,an+1-2an=(n+2)/n/(n+1),则a2,a3,a4,分别为多少,猜想an=

人气：301 ℃　时间：2020-05-27 07:12:13

解答

an+1-2an=(n+2)/(n(n+1)) an+1=2an+(n+2)/n*(n+1)=2an+(n+2)/n-(n+2)/(n+1)=2an+2/n-1/(n+1)an+1+1/(n+1)=2*(an+1/n)所以：{an+1/n}为等比数列,公比为2,首项为a1+1/1=1+1=2an+1/n=2*2^(n-1)=2^nan=2^n-1/n当n=1,a1=1...