设正数数列{an },{bn}满足:a1=b1=1,bn=an bn-1-1/4(n≥2).
求4+1/(a1 a2⋯ak )的最小值,其中m是给定的正整数.
设正数数列{an },{bn}满足:a1=b1=1,bn=an bn-1-1/4(n≥2).
求4+1/(a1 a2⋯ak )的最小值,其中m是给定的正整数.
由假设an=(bn+1/4)/bn-1 ,n≥2,于是a1 a2⋯an=((b2+1/4)(b3+1/4)⋯(bn+1/4))/(b1 b2⋯bn-1 ),即bn/(a1 a2⋯an )=bn/(a2⋯an )=(b2⋯bn)/((b2+1/4)(b3+1/4)⋯(bn+1/4))=1/((1+1/(4b2 ))(1+1/(4b3 ))⋯(1+1/(4bn )))≤又1/(a1 a2⋯ak )=1/a1 +1/(a1 a2⋯ak )=1+1/(a1 a2⋯a...
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