数列{an}满足a1=1,an=1/2an-1+1(n≥2)1.若bn=an-2,求证{bn}为等比数列2.求{an}的通项公式字母后的是下标..n-1是下标
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![数列{an}满足a1=1,an=1/2an-1+1(n≥2)1.若bn=an-2,求证{bn}为等比数列2.求{an}的通项公式字母后的是下标..n-1是下标](/uploads/image/z/5479482-66-2.jpg?t=%E6%95%B0%E5%88%97%7Ban%7D%E6%BB%A1%E8%B6%B3a1%3D1%2Can%3D1%2F2an-1%2B1%28n%E2%89%A52%291.%E8%8B%A5bn%EF%BC%9Dan%EF%BC%8D2%2C%E6%B1%82%E8%AF%81%EF%BD%9Bbn%EF%BD%9D%E4%B8%BA%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%972%EF%BC%8E%E6%B1%82%EF%BD%9Ban%EF%BD%9D%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%E5%AD%97%E6%AF%8D%E5%90%8E%E7%9A%84%E6%98%AF%E4%B8%8B%E6%A0%87%EF%BC%8E%EF%BC%8En-1%E6%98%AF%E4%B8%8B%E6%A0%87)
数列{an}满足a1=1,an=1/2an-1+1(n≥2)1.若bn=an-2,求证{bn}为等比数列2.求{an}的通项公式字母后的是下标..n-1是下标
数列{an}满足a1=1,an=1/2an-1+1(n≥2)
1.若bn=an-2,求证{bn}为等比数列2.求{an}的通项公式
字母后的是下标..n-1是下标
数列{an}满足a1=1,an=1/2an-1+1(n≥2)1.若bn=an-2,求证{bn}为等比数列2.求{an}的通项公式字母后的是下标..n-1是下标
1.an-2=1/2an-1-1=1/2(an-1-2)
∴(an-2)/(an-1-2)=1/2
即bn/bn-1=1/2
又有a1=1 b1=-1
∴{bn}为首项b1=-1,公比是1/2的等比数列
2.由上题知,{bn}通项公式为bn=-(1/2)^(n-1)
带入bn=an-2得 an=2-(1/2)^(n-1) (n≥2)
a=1时不成立 此时a1=1
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