求证:2/X*X-1 + 4/x*x-4 + 6/x*x-9 + .+ 20/x*x-100 = 11/(x-1)(x+10) + 11/(x-2)(x+9) + .+ 11/(x-10)(x+1)

题目

求证:2/X*X-1 + 4/x*x-4 + 6/x*x-9 + .+ 20/x*x-100 = 11/(x-1)(x+10) + 11/(x-2)(x+9) + .+ 11/(x-10)(x+1)
求证:2/(X*X-1) + 4/(x*x-4) + 6/(x*x-9) + ......+ 20/(x*x-100) = 11/(x-1)(x+10) + 11/(x-2)(x+9) + .....+ 11/(x-10)(x+1)

答案

因为 2n/(x²-n²)=1/(x-n)+1/(x+n)
所以左边=1/(x-1)+1/(x+1)+1/(x-2)+1/(x+2)+……+1/(x-10)+1/(x+10),
再根据右边式子的分母两两合并一下就变成右边的式子了.