1/(1*2)+1/(2*3)+1/(3*4).1/(199*200)

问题描述:

1/(1*2)+1/(2*3)+1/(3*4).1/(199*200)
脱式计算

裂项法:
1/(1*2)+1/(2*3)+1/(3*4).1/(199*200)
=1-1/2+1/2-1/3+1/3-1/4+……+1/199-1/200
=1-1/200
=199/200