已知M,N都是正整数,并且A=(1-1/2)(1+1/2)(1-1/3)(1+1/3)...(1-1/m)(1+1/m),5已知M,N都是正整数,并且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/n)(1+1/n).若a-b=1/26,求m和n的值.
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已知M,N都是正整数,并且A=(1-1/2)(1+1/2)(1-1/3)(1+1/3)...(1-1/m)(1+1/m),5已知M,N都是正整数,并且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/n)(1+1/n).若a-b=1/26,求m和n的值.
已知M,N都是正整数,并且A=(1-1/2)(1+1/2)(1-1/3)(1+1/3)...(1-1/m)(1+1/m),
5
已知M,N都是正整数,并且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/n)(1+1/n).若a-b=1/26,求m和n的值.
已知M,N都是正整数,并且A=(1-1/2)(1+1/2)(1-1/3)(1+1/3)...(1-1/m)(1+1/m),5已知M,N都是正整数,并且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/n)(1+1/n).若a-b=1/26,求m和n的值.
A=(1-1/2)(1+1/2)(1-1/3)(1+1/3)...(1-1/m)(1+1/m),
=(1-1/2)(1-1/3)(1-1/4)……(1-1/m)*(1+1/2)(1+1/3)(1+1/4)……(1+1/m)
=1/2 *2/3*3/4*……(m-1)/m *3/2*4/3*5/4……(m+1)/m
=1/m *(m+1)/2
=(m+1)/2m
=1/2+1/2m
同理,B=(n+1)/2n=1/2+1/2n
a-b=1/2m-1/2n=1/26
1/m-1/n=1/13
显然,m小于13
可以经过尝试得正整数解只有
m=12
n=156