已知数列{an}满足a1=2,an=2An-1+2的n+1次方++(1)若bn=2的n次方分之b的n次方,求证{bn}为等差数列{2}求{an}的通项公式
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已知数列{an}满足a1=2,an=2An-1+2的n+1次方++(1)若bn=2的n次方分之b的n次方,求证{bn}为等差数列{2}求{an}的通项公式已知数列{an}满足a1=2,an=2An-1
已知数列{an}满足a1=2,an=2An-1+2的n+1次方++(1)若bn=2的n次方分之b的n次方,求证{bn}为等差数列{2}求{an}的通项公式
已知数列{an}满足a1=2,an=2An-1+2的n+1次方++(1)若bn=2的n次方分之b的n次方,求证{bn}为等差数列
{2}求{an}的通项公式
已知数列{an}满足a1=2,an=2An-1+2的n+1次方++(1)若bn=2的n次方分之b的n次方,求证{bn}为等差数列{2}求{an}的通项公式
先证明
bn=b^n/2^n=(b/2)^n (1)
bn-1=(b/2)^(n-1) (2)
(1)÷(2)
bn/bn-1=b/2,是定值
所以bn是等比数列
计算an
an=2an-1+2^(n+1)
an=2an-1+2*2^n
两边都除以2^2
an/2^n-an-1*2/2^n=2
an/2^n-an-1/2^(n-1)=2
另Cn=an/2^n (n>=2)
Cn是等差数列
a1=2,a2=12
Cn=a2+(n-1)*2
an/2^n=12+2*(n-1)=2n+10
an=(2n+10)*2^n
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