已知数列﹛㏒₂﹙An-1﹚﹜(n∈正整数)为等差数列,且a1=3,a3=9,(1)、求数列{An}的通项公式(2)、证明1/(a2-a1)+1/(a3-a2)+……+1/(a( n+1) - an)<1
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![已知数列﹛㏒₂﹙An-1﹚﹜(n∈正整数)为等差数列,且a1=3,a3=9,(1)、求数列{An}的通项公式(2)、证明1/(a2-a1)+1/(a3-a2)+……+1/(a( n+1) - an)<1](/uploads/image/z/8668672-16-2.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%EF%B9%9B%E3%8F%92%26%238322%3B%EF%B9%99An-1%EF%B9%9A%EF%B9%9C%EF%BC%88n%E2%88%88%E6%AD%A3%E6%95%B4%E6%95%B0%EF%BC%89%E4%B8%BA%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2C%E4%B8%94a1%3D3%2Ca3%3D9%2C%EF%BC%881%EF%BC%89%E3%80%81%E6%B1%82%E6%95%B0%E5%88%97%EF%BD%9BAn%EF%BD%9D%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%EF%BC%882%EF%BC%89%E3%80%81%E8%AF%81%E6%98%8E1%2F%28a2-a1%29%2B1%2F%28a3-a2%29%2B%E2%80%A6%E2%80%A6%2B1%2F%28a%28+n%2B1%29+-+an%29%EF%BC%9C1)
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已知数列﹛㏒₂﹙An-1﹚﹜(n∈正整数)为等差数列,且a1=3,a3=9,(1)、求数列{An}的通项公式(2)、证明1/(a2-a1)+1/(a3-a2)+……+1/(a( n+1) - an)<1
已知数列﹛㏒₂﹙An-1﹚﹜(n∈正整数)为等差数列,且a1=3,a3=9,
(1)、求数列{An}的通项公式
(2)、证明1/(a2-a1)+1/(a3-a2)+……+1/(a( n+1) - an)<1
已知数列﹛㏒₂﹙An-1﹚﹜(n∈正整数)为等差数列,且a1=3,a3=9,(1)、求数列{An}的通项公式(2)、证明1/(a2-a1)+1/(a3-a2)+……+1/(a( n+1) - an)<1
a1=3,a3=9 a1-1=2 a3-1=8
设bn=﹛㏒₂﹙An-1﹚﹜
b1=1, b3=3 2d=3-1 d=1
bn=1+n-1=n ==﹛㏒₂﹙An-1﹚﹜
An=2^n+1
2.an+1-an=2^n
1/(a2-a1)+1/(a3-a2)+……+1/(a( n+1) - an)
=1/2+1/4+1/8+.+1/2^n
=1-1/[2^(n+1)]
(1)、数列{An}的通项公式An=1+2^n,
(2)、证明1/(a2-a1)+1/(a3-a2)+……+1/(a( n+1) - an)<1,1/(a( n+1) - an)=1/2^n,∴1/2+1/4+1/8+1/16+……+1/2^n=1-1/2^n<1.