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.
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/11 18:19:07
![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.](/uploads/image/z/6894672-24-2.jpg?t=%E5%B7%B2%E7%9F%A5M%2CN%E9%83%BD%E6%98%AF%E6%AD%A3%E6%95%B4%E6%95%B0%2C%E5%B9%B6%E4%B8%94A%3D%EF%BC%881-1%2F2%EF%BC%89%EF%BC%881%2B1%2F2%29%281-1%2F3%29%281%2B1%2F3%29...%281-1%2Fm%29%281%2B1%2Fm%29%2C5%E5%B7%B2%E7%9F%A5M%2CN%E9%83%BD%E6%98%AF%E6%AD%A3%E6%95%B4%E6%95%B0%2C%E5%B9%B6%E4%B8%94A%3D%EF%BC%881-1%2F2%EF%BC%89%EF%BC%881%2B1%2F2%29%281-1%2F3%29%281%2B1%2F3%29...%281-1%2Fm%29%281%2B1%2Fm%29%2CB%3D%281-1%2F2%29%281%2B1%2F2%29%281-1%2F3%29%281%2B1%2F3%29...%EF%BC%881-1%2Fn%29%281%2B1%2Fn%29.%E8%8B%A5a-b%3D1%2F26%2C%E6%B1%82m%E5%92%8Cn%E7%9A%84%E5%80%BC.)
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