(1+1/1×3)(1+1/2×4)(1+1/3×5)……(1+1/49×51)

问题描述:

(1+1/1×3)(1+1/2×4)(1+1/3×5)……(1+1/49×51)

原式=2^2/((2-1)*(2+1))*3^2/((3-1)*(3+1))*…*50^2/((50-1)*(50+1))
=2/1*2/3*3/2*3/4*…*50/49*50/51
=2*50/51
=100/51