对所有x=-1且x≠-2的值,等式1/(x+1)(x+2)=A/(x+1) +B/(x+2)恒成立,求A、B的值应用以上结论计算：_数学解答

对所有x=-1且x≠-2的值,等式1/(x+1)(x+2)=A/(x+1) +B/(x+2)恒成立,求A、B的值
应用以上结论计算：1/(1*2) +1/(2*3) +1/(3*4)...+1/(99*100)

人气：150 ℃　时间：2020-06-21 15:58:19

解答

A/(x+1) +B/(x+2) =[A(x+2)+B(x+1)]/(x+1)(x+2) =[(A+B)x+(2A+B)]/(x+1)(x+2) =1/(x+1)(x+2) 所以(A+B)x+(2A+B)=1=0*x+1 所以A+B=0 2A+B=1 相减 A=1,B=-A=-1 1/(x+1)(x+2) =[(x+2)-(x+1)]/(x+1)(x+2) =(x+2)/(x+1)(x...