Question

计算1/1*3+1/2*4+1/3*5+.+1/18*20

Answer 1

1/1*3+1/2*4+1/3*5+.+1/18*20=[1/1*3+1/3*5+...+1/17*19]+[1/2*4+1/4*6+...+1/18*20]=[(1-1/3)/2+(1/3-1/5)/2+...+(1/17-1/19)/2]+[(1/2-1/4)/2+(1/4-1/6)/2+...+(1/18-1/20)/2]=(1+1/2-1/19-1/20)/2=531/760