Question

1/1×2×3+1/2×3×4+1/3×4×5+.+1/48×49×50

Answer 1

1/1*3+1/2*4+1/3*5+.+1/48*50=?

1/n(n+2)=[(1/n-1/(n+2)]/2

原式

=[(1/1-1/3)+(1/2-1/4)+……(1/48-1/50)]/2

=(1+1/2-1/49-1/50)/2

=1788/2450

=894/1225