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.
问题描述:
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.
答
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+1/2...