题目
证明题2/(x^2-1)+4/(x^2-4)+...+20/(x^2-100)=11/(x-1)(x+10)+11/(x-2)(x+9)+...+11/(x-10)(x+1)
2/(x^2-1)+4/(x^2-4)+6/(x^2-9)+...+20/(x^2-100)=11/(x-1)(x+10)+11/(x-2)(x+9)+...+11/(x-10)(x+1)
2/(x^2-1)+4/(x^2-4)+6/(x^2-9)+...+20/(x^2-100)=11/(x-1)(x+10)+11/(x-2)(x+9)+...+11/(x-10)(x+1)
提问时间:2021-03-29
答案
左边
2/(x^2-1)=1/(x-1)-1/(x+1)
4/(x^2-4)=1/(x-2)-1/(x+2)
.
20/(x^2-20)=1/(x-10)-1/(x+10)
右边
11/(x-1)(x+10)=1/(x-1)-1/(x+10)
.
11/(x-10)(x+1)=1/(x-10)-1/(x+1)
左边右边都=1/(x-1)+1/(x-2)+1/(x-3)+1/(x-4)+1/(x-5)+1/(x-6)+1/(x-7)+1/(x-8)+1/(x-9)+1/(x-10/)-1/(x+1)-1/(x+2)-1/(x+3)-1/(x+4)-1/(x+5)-1/(x+6)-1/(x+7)-1/(x+8)-1/(x+9)-1/(x+10)
2/(x^2-1)=1/(x-1)-1/(x+1)
4/(x^2-4)=1/(x-2)-1/(x+2)
.
20/(x^2-20)=1/(x-10)-1/(x+10)
右边
11/(x-1)(x+10)=1/(x-1)-1/(x+10)
.
11/(x-10)(x+1)=1/(x-10)-1/(x+1)
左边右边都=1/(x-1)+1/(x-2)+1/(x-3)+1/(x-4)+1/(x-5)+1/(x-6)+1/(x-7)+1/(x-8)+1/(x-9)+1/(x-10/)-1/(x+1)-1/(x+2)-1/(x+3)-1/(x+4)-1/(x+5)-1/(x+6)-1/(x+7)-1/(x+8)-1/(x+9)-1/(x+10)
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