计算：1/2根号1+1×根号2+1/3根号2+2根号3+.1/（n+1）×根号n+n×根号n+1
问题描述：
计算：1/2根号1+1×根号2+1/3根号2+2根号3+.1/（n+1）×根号n+n×根号n+1
答
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]=√...