求和:(1/1*2)+
(1/ 1*2 ) + (1/ 2*3)+ (1/ 3*4)+……+(1/ 2017*2018)
=1-1/2+1/2-1/3+1/3-1/4+.......+1/2017-1/2018
=1-1/2018
=2017/2018
您好:
裂项法。
(1/ 1*2 ) + (1/ 2*3)+ (1/ 3*4)+……+(1/ 2017*2018)
=(1/ 1-1/2 ) + (1/ 2-1/3)+ (1/ 3-1/4)+……+(1/ 2017-1/2018)
=1/ 1-1/2 + 1/ 2-1/3+ 1/ 3-1/4+……+1/ 2017-1/2018
=1-1/2018
=2017/2018
热门标签: