壹.1×2+2×3+3×4+...+100×101=?

题目

壹.1×2+2×3+3×4+...+100×101=?
贰.1×2+2×3+3×4+...+n(n+1)=?
叁.1×2×3+2×3×4+...+n(n+1)(n+2)=?
明天就要交了

答案

壹.1×2+2×3+3×4+...+100×101
=1/3*1*2*3+1/3(2*3*4-1*2*3)+1/3(3*4*5-2*3*4)+...+1/3(100*101*102-99*100*101)
=1/3(1*2*3+2*3*4-1*2*3+3*4*5-2*3*4+.+100*101*102-99*100*101)
=1/3*100*101*102
=343400
贰.1×2+2×3+3×4+...+n(n+1)=?
=1/3n(n+1)(n+2)
叁.1×2×3+2×3×4+...+n(n+1)(n+2)=?
=1/4n(n+1)(n+2)(n+3)