1/1×2×3×4+1/2×3×4×5+…+1/10×11×12×13+1/11×12×13×14怎样计算

来源：百度知道编辑：UC知道时间：2024/09/28 10:29:56

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)]
=(1/3)*[1/(1*2*3)-1/(2*3*4)+1/(2*3*4)-1/(3*4*5)+...+1/(10*11*12)-1/(11*12*13)+1/(11*12*13)-1/(12*13*14)]
=(1/3)*[1/(1*2*3)-1/(12*13*14)]
=(1/3)*{(1/2)*[1/(1*2)-1/(2*3)]-(1/2)*[1/(12*13)-1/(13*14)]}
=(1/3)*(1/2)*(1/1-1/2-1/2+1/3-1/12+1/13+1/13-1/14)
=(1/6)*(121/364)
=121/2184.

6Cn+3n/n

(1+1/2+1/3+1/4)× 1+1/2+1+1/3+1+1/4+......+1/100=? (1-1/2)(1-1/3)(1-1/4)(1-1/5).....(1-1/1000) (1-1/2^2)*(1-1/3^2)*(1-1/4^2).......(1-1/100^2) 1/1+1/2+1/3+1/4+。。。。+1/N 是多少 1/1+1/2+1/3+1/4+......1/2002＝？ 1-1/2+1/3-1/4+........1/99-1/100 1/1*2+1/2*3+1/3*4+...+1/99*100 1/1*2+1/2*3+1/3*4+..........+1/2002*2003 1*(1/2)+2*(1/3)+3*(1/4)+...+99*(1/100)