1)已知数列{An}满足:An+2/A(n-1)=3 (n大于等于2) A1=32)已知数列{An}满足:A1=1/2,AnA(n+1)=An-A(n+1)3)已知数列{An}满足:A1=1,A(n+1)=2An+3第一小题没看懂诶 下标的 和别的加一减一搞不清楚了
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 02:06:57
![1)已知数列{An}满足:An+2/A(n-1)=3 (n大于等于2) A1=32)已知数列{An}满足:A1=1/2,AnA(n+1)=An-A(n+1)3)已知数列{An}满足:A1=1,A(n+1)=2An+3第一小题没看懂诶 下标的 和别的加一减一搞不清楚了](/uploads/image/z/1085329-1-9.jpg?t=1%EF%BC%89%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7BAn%7D%E6%BB%A1%E8%B6%B3%EF%BC%9AAn%2B2%2FA%28n-1%29%3D3+%EF%BC%88n%E5%A4%A7%E4%BA%8E%E7%AD%89%E4%BA%8E2%EF%BC%89+A1%3D32%29%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7BAn%7D%E6%BB%A1%E8%B6%B3%EF%BC%9AA1%3D1%2F2%2CAnA%28n%2B1%29%3DAn-A%28n%2B1%293%29%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7BAn%7D%E6%BB%A1%E8%B6%B3%3AA1%3D1%2CA%28n%2B1%29%3D2An%2B3%E7%AC%AC%E4%B8%80%E5%B0%8F%E9%A2%98%E6%B2%A1%E7%9C%8B%E6%87%82%E8%AF%B6+%E4%B8%8B%E6%A0%87%E7%9A%84+%E5%92%8C%E5%88%AB%E7%9A%84%E5%8A%A0%E4%B8%80%E5%87%8F%E4%B8%80%E6%90%9E%E4%B8%8D%E6%B8%85%E6%A5%9A%E4%BA%86)
1)已知数列{An}满足:An+2/A(n-1)=3 (n大于等于2) A1=32)已知数列{An}满足:A1=1/2,AnA(n+1)=An-A(n+1)3)已知数列{An}满足:A1=1,A(n+1)=2An+3第一小题没看懂诶 下标的 和别的加一减一搞不清楚了
1)已知数列{An}满足:An+2/A(n-1)=3 (n大于等于2) A1=3
2)已知数列{An}满足:A1=1/2,AnA(n+1)=An-A(n+1)
3)已知数列{An}满足:A1=1,A(n+1)=2An+3
第一小题没看懂诶 下标的 和别的加一减一搞不清楚了
1)已知数列{An}满足:An+2/A(n-1)=3 (n大于等于2) A1=32)已知数列{An}满足:A1=1/2,AnA(n+1)=An-A(n+1)3)已知数列{An}满足:A1=1,A(n+1)=2An+3第一小题没看懂诶 下标的 和别的加一减一搞不清楚了
1) An-1=2-2/An-1=2(A(n-1)-1)/A(n-1)
An-2=1-2/An-1=(A(n-1)-2)/A(n-1)
两式相除得
(An-1)/(An-2)=2(A(n-1)-1)/(A(n-1)-2)
设Bn=(An-1)/(An-2)
Bn成等比 B1=(3-1)/(3-2)=2
Bn=2*2^(n-1)=2^n
(An-1)/(An-2)=2^n
An=(2^(n+1)+1)/(2^n-1)
2)两边除以AnAn+1得
1=1/An+1-1/An
bn=1/An
bn成等差
b1=2
bn=2+(n-1)=n+1
An=1/(n+1)
3)An+1+1=2(An+1)
bn=An+1
bn成等比
b1=2
bn=2^n
An=2^n-1