①1/(2+√2)+1/(3√2+2√3)+1/(4√3+3√4)+...+1/(2007√2006+2006√2007)
问题描述：
①1/(2+√2)+1/(3√2+2√3)+1/(4√3+3√4)+...+1/(2007√2006+2006√2007)
②求y=1-2x+2√(4x-3)的最大值
答
① 设有a、b两数,a-b=1,则有1/(a√b+b√a) = (a√b-b√a) /(a^2 b + b^2 a)= (a√b-b√a)/1/(ab(a-b)） = 1/√b - 1/√a所以1/(2+√2)+1/(3√2+2√3)+1/(4√3+3√4)+...+1/(2007√2006+2006√2007)= 1/√1- 1/√2 + ...