1-1/2+1/3-1/4+‥‥+1/99-1/100
=(1+1/3+1/5+‥‥1/99) - (1/2+1/4+‥‥+1/100)
=(1+1/2+1/3+1/4+‥‥+1/99+1/100) - 2(1/2+1/4+‥‥+1/100)
=(1+1/2+1/3+1/4+‥‥+1/99+1/100) - (1+1/2+‥‥+1/50)
=1/51+1/52+‥‥+1/99+1/100
=(1/51+1/100)+(1/52+1/99)+‥‥(1/75+1/76)
=151/(51*100)+151/(52*99)+‥‥+151/(75*76)
151は素数なので、分母を通分しても出てこない。