(1+1/2+1/3+...+1/99)×(1/2+1/3+1/4+...+1/100)—(1+1/2+1/3+1/4+...14/100)×(1/2+1/3+...+1/99)=

问题描述:

(1+1/2+1/3+...+1/99)×(1/2+1/3+1/4+...+1/100)—(1+1/2+1/3+1/4+...14/100)×(1/2+1/3+...+1/99)=

令a=1/2+1/3+...+1/99
原式=(1+a)(a+1/100)-a(1+a+1/100)
=a(1+a)+1/100(1+a)-a(1+a)-1/100a
=1/100(1+a)-1/100a
=1/100+1/100a-1/100a
=1/100