数列{an}满足a1=1,an=1/2a(n-1)1(n≥2)(1)若bn=an-2,求证{bn}为等比数列(2)求{an}的通项公式更正:将“n=1/2a(n-1)1”改为“an=1/2a(n-1)+1”
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![数列{an}满足a1=1,an=1/2a(n-1)1(n≥2)(1)若bn=an-2,求证{bn}为等比数列(2)求{an}的通项公式更正:将“n=1/2a(n-1)1”改为“an=1/2a(n-1)+1”](/uploads/image/z/7646318-62-8.jpg?t=%E6%95%B0%E5%88%97%EF%BD%9Ban%EF%BD%9D%E6%BB%A1%E8%B6%B3a1%3D1%2Can%3D1%2F2a%28n-1%291%28n%E2%89%A52%29%EF%BC%881%EF%BC%89%E8%8B%A5bn%3Dan-2%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%97%EF%BC%882%EF%BC%89%E6%B1%82%EF%BD%9Ban%EF%BD%9D%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%E6%9B%B4%E6%AD%A3%EF%BC%9A%E5%B0%86%E2%80%9Cn%3D1%2F2a%28n-1%291%E2%80%9D%E6%94%B9%E4%B8%BA%E2%80%9Can%3D1%2F2a%28n-1%29%2B1%E2%80%9D)
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数列{an}满足a1=1,an=1/2a(n-1)1(n≥2)(1)若bn=an-2,求证{bn}为等比数列(2)求{an}的通项公式更正:将“n=1/2a(n-1)1”改为“an=1/2a(n-1)+1”
数列{an}满足a1=1,an=1/2a(n-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
更正:将“n=1/2a(n-1)1”改为“an=1/2a(n-1)+1”
数列{an}满足a1=1,an=1/2a(n-1)1(n≥2)(1)若bn=an-2,求证{bn}为等比数列(2)求{an}的通项公式更正:将“n=1/2a(n-1)1”改为“an=1/2a(n-1)+1”
应该是an=1/2a(n-1)+1吧
an-2=1/2(a(n-1)-2)
bn=1/2b(n-1)因此bn等比
b1=-1
bn=-(1/2)^(n-1)
an=bn+2=-(1/2)^(n-1)+2
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