1/(2√1+1√2)=1*(2√1-1√2)/[(2√1+1√2)(2√1-1√2)]=(2√1-1√2)/[(2√1)²-(1√2)²]=√1/1-√2/2,1/(3√2+2√3)=1*(3√2-2√3)/[(3√2+2√3)(3√2-2√3)]=(3√2-2√3)/[(3√2)²-(2√3)²]=√2/2-√3/3,oswakos。。。。1/[2√1+1√2]+1/[3√2+2√3]+...........1/[(n+1)√n+n√n+1]= √1/1-√2/3+ √2/2-√3/3+...+√n/n-√(n+1)/(n+1)=1-√(n+1)/(n+1) 有疑问057请追问;若满意aeim请采纳,谢谢!