设数列A1,A2,...,An...前n项和Sn与An的关系是Sn=kAn+1.急设数列A1,A2,...,An...前n项和Sn与An的关系是Sn=kAn+1(k是与n无关的实数,k不等于1)(1)试写An(用n、k表示)(2)limSn=1,求k的取值范围
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![设数列A1,A2,...,An...前n项和Sn与An的关系是Sn=kAn+1.急设数列A1,A2,...,An...前n项和Sn与An的关系是Sn=kAn+1(k是与n无关的实数,k不等于1)(1)试写An(用n、k表示)(2)limSn=1,求k的取值范围](/uploads/image/z/11496491-35-1.jpg?t=%E8%AE%BE%E6%95%B0%E5%88%97A1%2CA2%2C...%2CAn...%E5%89%8Dn%E9%A1%B9%E5%92%8CSn%E4%B8%8EAn%E7%9A%84%E5%85%B3%E7%B3%BB%E6%98%AFSn%3DkAn%2B1.%E6%80%A5%E8%AE%BE%E6%95%B0%E5%88%97A1%2CA2%2C...%2CAn...%E5%89%8Dn%E9%A1%B9%E5%92%8CSn%E4%B8%8EAn%E7%9A%84%E5%85%B3%E7%B3%BB%E6%98%AFSn%3DkAn%2B1%28k%E6%98%AF%E4%B8%8En%E6%97%A0%E5%85%B3%E7%9A%84%E5%AE%9E%E6%95%B0%2Ck%E4%B8%8D%E7%AD%89%E4%BA%8E1%29%EF%BC%881%EF%BC%89%E8%AF%95%E5%86%99An%EF%BC%88%E7%94%A8n%E3%80%81k%E8%A1%A8%E7%A4%BA%EF%BC%89%EF%BC%882%EF%BC%89limSn%3D1%2C%E6%B1%82k%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4)
设数列A1,A2,...,An...前n项和Sn与An的关系是Sn=kAn+1.急设数列A1,A2,...,An...前n项和Sn与An的关系是Sn=kAn+1(k是与n无关的实数,k不等于1)(1)试写An(用n、k表示)(2)limSn=1,求k的取值范围
设数列A1,A2,...,An...前n项和Sn与An的关系是Sn=kAn+1.急
设数列A1,A2,...,An...前n项和Sn与An的关系是Sn=kAn+1(k是与n无关的实数,k不等于1)
(1)试写An(用n、k表示)
(2)limSn=1,求k的取值范围
设数列A1,A2,...,An...前n项和Sn与An的关系是Sn=kAn+1.急设数列A1,A2,...,An...前n项和Sn与An的关系是Sn=kAn+1(k是与n无关的实数,k不等于1)(1)试写An(用n、k表示)(2)limSn=1,求k的取值范围
Sn=KAn+1
Sn-1=KAn-1+1
An=kAn-KAn-1
An=KAn-1/(k-1)
所以An是公比为k/(k-1)的等比数列
a1=ka1+1
a1=1/(1-k)
Sn=a1(q^n-1)/(q-1)=[(k/k-1)^n-1]/[(1-k)(k/k-1-1)]
=1-(k/k-1)^n
limSn=1
lim(k/k-1)^n=0
-1
(1) Sn=kAn+1;
Sn_1=kAn_1+1;
An=Sn-Sn_1;
An=kAn-kAn_1;
(k-1)An=kAn_1;
An/An_1=k/(k-1);
哦你没有告诉我A1是好多呢?不过没关系
答案是:An=[k/(k-1)]的n-1次方乘以A...
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(1) Sn=kAn+1;
Sn_1=kAn_1+1;
An=Sn-Sn_1;
An=kAn-kAn_1;
(k-1)An=kAn_1;
An/An_1=k/(k-1);
哦你没有告诉我A1是好多呢?不过没关系
答案是:An=[k/(k-1)]的n-1次方乘以A1;
(2)根据等比求和公式,得到
Sn=[[k/(k-1)]的n次方-1]A1(k-1);
哦太难计算了!!
不好意思!
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