等比数列等差数列习题1.已知{An},A1=2,An=2(An-1)-1,n大于等于2,求An.(“n-1”为下 标)2.已知{An}中,A1=1,(An+1)-An=3^n-n,求通项公式.(“n+1”为 下标)3.已知{An}满足An+1=2^n乘An,且A1=1,求An.(“n
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/14 01:05:32
![等比数列等差数列习题1.已知{An},A1=2,An=2(An-1)-1,n大于等于2,求An.(“n-1”为下 标)2.已知{An}中,A1=1,(An+1)-An=3^n-n,求通项公式.(“n+1”为 下标)3.已知{An}满足An+1=2^n乘An,且A1=1,求An.(“n](/uploads/image/z/693503-71-3.jpg?t=%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%E4%B9%A0%E9%A2%981.%E5%B7%B2%E7%9F%A5%7BAn%7D%2CA1%3D2%2CAn%3D2%EF%BC%88An-1%EF%BC%89-1%2Cn%E5%A4%A7%E4%BA%8E%E7%AD%89%E4%BA%8E2%2C%E6%B1%82An.%EF%BC%88%E2%80%9Cn-1%E2%80%9D%E4%B8%BA%E4%B8%8B++++%E6%A0%87%EF%BC%892.%E5%B7%B2%E7%9F%A5%7BAn%7D%E4%B8%AD%2CA1%3D1%2C%EF%BC%88An%2B1%EF%BC%89-An%3D3%5En-n%2C%E6%B1%82%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F.%EF%BC%88%E2%80%9Cn%2B1%E2%80%9D%E4%B8%BA++%E4%B8%8B%E6%A0%87%EF%BC%893.%E5%B7%B2%E7%9F%A5%7BAn%7D%E6%BB%A1%E8%B6%B3An%2B1%3D2%5En%E4%B9%98An%2C%E4%B8%94A1%3D1%2C%E6%B1%82An.%EF%BC%88%E2%80%9Cn)
等比数列等差数列习题1.已知{An},A1=2,An=2(An-1)-1,n大于等于2,求An.(“n-1”为下 标)2.已知{An}中,A1=1,(An+1)-An=3^n-n,求通项公式.(“n+1”为 下标)3.已知{An}满足An+1=2^n乘An,且A1=1,求An.(“n
等比数列等差数列习题
1.已知{An},A1=2,An=2(An-1)-1,n大于等于2,求An.(“n-1”为下
标)
2.已知{An}中,A1=1,(An+1)-An=3^n-n,求通项公式.(“n+1”为
下标)
3.已知{An}满足An+1=2^n乘An,且A1=1,求An.(“n+1”为下标)
麻烦写出详细过程,该转行的地方请转行,不然不方便看清
等比数列等差数列习题1.已知{An},A1=2,An=2(An-1)-1,n大于等于2,求An.(“n-1”为下 标)2.已知{An}中,A1=1,(An+1)-An=3^n-n,求通项公式.(“n+1”为 下标)3.已知{An}满足An+1=2^n乘An,且A1=1,求An.(“n
(1)∵a[1]=2,a[n]=2a[n-1]-1,n≥2
∴a[n]-1=2(a[n-1]-1) n≥2
∵a[1]-1=1
∴{a[n]-1}是首项为1公比为2的等比数列
∵a[n]-1=2^(n-1)
∴a[n]=2^(n-1)+1
(2)∵a[1]=1,a[n+1]-a[n]=3^n-n
∴a[n]-a[n-1]=3^(n-1)-(n-1)
.
a[3]-a[2]=3^2-2
a[2]-a[1]=3^1-1
上述各项叠加:
a[n]-a[1]=[(3^1+3^2+...+3^(n-1)]-[1+2+...+(n-1)]
∴a[n]=3[3^(n-1)-1]/2-n(n-1)/2+1
(3)∵a[n+1]=2^n*a[n],且a[1]=1
∴a[n+1]/a[n]=2^n
∵a[n]=(a[n]/a[n-1])(a[n-1]/a[n-2])...(a[3]/a[2])(a[2]/a[1])a[1]
∴a[n]=2^(n-1)*2^(n-2)*...*2^2*2^1
=2^[(n-1)+(n-1)+...+2+1]
=2^[n(n-1)/2]