求证明(1+1/3)*(1+1/5)*****(1+1/(2n-1))〉1/2*√(2n+1)
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求证明(1+1/3)*(1+1/5)*****(1+1/(2n-1))〉1/2*√(2n+1)
求证明(1+1/3)*(1+1/5)*****(1+1/(2n-1))〉1/2*√(2n+1)
求证明(1+1/3)*(1+1/5)*****(1+1/(2n-1))〉1/2*√(2n+1)
1+1/3>1+1/4,1+1/5>1+1/6,.1+1/2n-1>1+1/2n
所以[(1+1/3)(1+1/5)...(1+1/2n-1)>]^2
>(1+1/3)(1+1/4)(1+1/5)(1+1/6)...(1+1/2n-1)(1+1/2n)= 2n+1)/3
>(2n+1)/4
两边开方
得(1+1/3)*(1+1/5)*****(1+1/(2n-1))〉1/2*√(2n+1)