(√2-1)(√2+1)=1,(√3-√2)(√3+√2)...利用上述规律运算

问题描述:

(√2-1)(√2+1)=1,(√3-√2)(√3+√2)...利用上述规律运算
(√2-1)(√2+1)=1,(√3-√2)(√3+√2)...
利用上述规律运算:(1/(1+√2)+1/(√2+√3)+...+1/(√2002+2003)(1+√2003)的值

(1/(1+√2)+1/(√2+√3)+...+1/(√2002+2003)(1+√2003)
=【√2-1+√3-√2+……+√2003-√2002】(1+√2003)
=(√2003 -1)×(1+√2003)
=2003-1
=2002