(1)3/2+7/6+13/12+21/20+...111/110 (2)1-2+3-4+.-200+201

问题描述:

(1)3/2+7/6+13/12+21/20+...111/110 (2)1-2+3-4+.-200+201

(1) 3/2+7/6+13/12+21/20+...111/110
=1+1/(1*2)+1+1/(2*3)+1+1/(3*4)+1+1/(4*5)+...+1+1/(10*11)
=10+1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+...+1/(10*11)
=10+(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+...+(1/10-1/11)
=10+1-1/11
=10又(10/11)
(2)1-2+3-4+.-200+201
=(1-2)+(3-4)+...+(199-200)+201
=-1*200/2 +201
=-100+201
=101