1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+……+1/(x+1997)(x+1998)=1/3x+5994,求x的值

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1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+……+1/(x+1997)(x+1998)=1/3x+5994,求x的值
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1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+……+1/(x+1997)(x+1998)=1/3x+5994,求x的值
1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+……+1/(x+1997)(x+1998)=1/3x+5994,求x的值

1/(x+1)(x+2)+1/(x+2)(x+3)+1/(x+3)(x+4)+……+1/(x+1997)(x+1998)=1/3x+5994,求x的值
图片上的过程之后 等式右边化为1/(3*(x+1998))
两边同时乘以(x+1998)得
(x+1998)/(x+1)=4/3 
解之得 x=5990