作业帮设正整数M,N满足M＜N,且1/(M²+M）+1/[（M+1）²+(M+1)]+...+1/(N²+N)=1/23,求M+N的值（求原式=1/M-1/(N+1)=1/23,答案为M+N=527辛苦了!
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![设正整数M,N满足M＜N,且1/(M²+M）+1/[（M+1）²+(M+1)]+...+1/(N²+N)=1/23,求M+N的值（求原式=1/M-1/(N+1)=1/23,答案为M+N=527辛苦了!](/uploads/image/z/671543-71-3.jpg?t=%E8%AE%BE%E6%AD%A3%E6%95%B4%E6%95%B0M%2CN%E6%BB%A1%E8%B6%B3M%EF%BC%9CN%2C%E4%B8%941%2F%28M%26%23178%3B%2BM%EF%BC%89%2B1%2F%5B%EF%BC%88M%2B1%EF%BC%89%26%23178%3B%2B%28M%2B1%29%5D%2B...%2B1%2F%28N%26%23178%3B%2BN%29%3D1%2F23%2C%E6%B1%82M%2BN%E7%9A%84%E5%80%BC%EF%BC%88%E6%B1%82%E5%8E%9F%E5%BC%8F%3D1%2FM-1%2F%28N%2B1%29%3D1%2F23%2C%E7%AD%94%E6%A1%88%E4%B8%BAM%2BN%3D527%E8%BE%9B%E8%8B%A6%E4%BA%86%21)
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设正整数M,N满足M＜N,且1/(M²+M）+1/[（M+1）²+(M+1)]+...+1/(N²+N)=1/23,求M+N的值（求原式=1/M-1/(N+1)=1/23,答案为M+N=527辛苦了!
设正整数M,N满足M＜N,且1/(M²+M）+1/[（M+1）²+(M+1)]+...+1/(N²+N)=1/23,求M+N的值（求
原式=1/M-1/(N+1)=1/23,答案为M+N=527
辛苦了!
设正整数M,N满足M＜N,且1/(M²+M）+1/[（M+1）²+(M+1)]+...+1/(N²+N)=1/23,求M+N的值（求原式=1/M-1/(N+1)=1/23,答案为M+N=527辛苦了!
1/(M²+M）这一项可以写成1/M(M+1),比如1/(2*3)可以写成1/2-1/3,也就是说,后面的项都可以这么写就有了,如果是数字的话,1/2-1/3+1/3-1/4+1/4-1/5.中间项消去就是1/2-1/5,这个题是字母表示的,结果就是1/M-1/(N+1).剩下的通分解个方程组就好