Question

1/4+1/12+1/24+1/40+……+1/19800=?

Answer 1

1/4+1/12+1/24+1/40+……+1/19800=(1/2)*[1/2+1/6+1/12+1/20+...+1/9900]=(1/2)*[1/1*2+1/2*3+1/3*4+1/4*5+...+1/99*100]=(1/2)*[1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/99-1/100]=(1/2)*[1-1/100]=(1/2)*(99/100)=99...