化简并计算1/√X(X+1)+1/(√X+1)(√X+2)乘以1/(√X+2)(√X+3)+……+ 1/(√X+19)(√X+20)=____结果中分母不含根式

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/29 03:48:41

化简并计算1/√X(X+1)+1/(√X+1)(√X+2)乘以1/(√X+2)(√X+3)+……+ 1/(√X+19)(√X+20)=____结果中分母不含根式
化简并计算1/√X(X+1)+1/(√X+1)(√X+2)乘以1/(√X+2)(√X+3)+……+ 1/(√X+19)(√X+20)=____
结果中分母不含根式

化简并计算1/√X(X+1)+1/(√X+1)(√X+2)乘以1/(√X+2)(√X+3)+……+ 1/(√X+19)(√X+20)=____结果中分母不含根式
=1/√x-1/(√x+1)+1/(√x+1)-1/(√x+2)+1/(√x+2)-……-1/(√x+19)+1/(√x+19)-1/(√x+20)
=1/√x-1/(√x+20)
=√x/x-(√x-20)/x-400
=(x√x-400√x-x√x+20x)/x(x-400)
=(20x-400√x)/x(x-400)

=(20x-400√x)/x(x-400)