1/1×2×3×4+1/2×3×4×5+…+1/10×11×12×13+1/11×12×13×14怎样计算
问题描述：
1/1×2×3×4+1/2×3×4×5+…+1/10×11×12×13+1/11×12×13×14怎样计算
答
1/(1×2×3×4)+1/(2×3×4×5)+…+1/(10×11×12×13)+1/(11×12×13×14)=(1/3)*[1/(1*2*3)-1/(2*3*4)]+(1/3)*[1/(2*3*4)-1/(3*4*5)]+...+(1/3)*[1/(10*11*12)-1/(11*12*13)]+(1/3)*[1/(11*12*13)-1/(12*13*14)]=(...