1/2根号1+1根号2+1/3根号2+2根号3+.+1/100根号99+99根号100.

问题描述:

1/2根号1+1根号2+1/3根号2+2根号3+.+1/100根号99+99根号100.

由1/(2√1+1√2)+1/(3√2+2√3)+1/(4√3+3√4)+...+1/(100√99+99√100)=(2√1-1√2)/(2√1+1√2)(2√1-1√2)+(3√2-2√3)/(3√2+2√3)(3√2-2√3)+(4√3-3√4)/(4√3+3√4)(4√3-3√4)+....