数列bn满足b1=1,b(n+1)=2bn+1,若数列an满足a1=1,an=bn[1/b1+1/b2+…+1/b(n-

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/17 18:57:57

数列bn满足b1=1,b(n+1)=2bn+1,若数列an满足a1=1,an=bn[1/b1+1/b2+…+1/b(n-1)],n≥2且n为正整数
证明(an+1)/a(n+1)=bn/b(n+1);证明(1+1/a1)(1+1/a2)…(1+1/an)

1=1,b=2bn+1,
∴b+1=2(bn+1),
∴bn+1=(b1+1)*2^(n-1)=2^n,
∴bn=2^n-1.
a=b(1/b1+1/b2+……+1/bn),
∴a/b=1/b1+1/b2+……+1/bn=an/bn+1/bn=(an+1)/bn,
∴（an+1)/a=bn/b.

n>=4时2^n>=n^,
1/bn

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