问题标题:
数学精英请进A=(1-1/2)(1+1/2)(1-1/3)(1+1/3)...(1-1/M)(1+1/M)B=(1-1/2)(1+1/2)(1-1/3)(1+1/3)...(1-1/K)(1+1/K)若A-B=1/26,求M和K的值?
问题描述:
数学精英请进
A=(1-1/2)(1+1/2)(1-1/3)(1+1/3)...(1-1/M)(1+1/M)B=(1-1/2)(1+1/2)(1-1/3)(1+1/3)...(1-1/K)(1+1/K)若A-B=1/26,求M和K的值?
潘兆鸿回答:
A=[(1+1/2)*(1+1/3)...(1+1/M)]*[(1-1/2)*(1-1/3)...(1-M/10)]=[(3/2)*(4/3)*(5/4)...(M+1)/M]*[(1/2)*(2/3)*(3/4)...(M-1)/M]=(M+1)/2*(1/M)=(M+1)/2M同理B=(K+1)/2KA-B=(M+1)/2M-(K+1)/2K=1...
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