现在急需的数学计算~~~⑴1*2+2*3+3*4+……+100*101=⑵1*2+2*3+3*4+……+n(n+1)=⑶

2个回答

  • n(n+1)=(n(n+1)(n+2)-(n-1)n(n+1))/3

    ⑵1*2+2*3+3*4+……+n(n+1)

    =(1*2*3-0*1*2)/3+(2*3*4-1*2*3)/3+(3*4*5-2*3*4)/3+...+(n(n+1)(n+2)-(n-1)n(n+1))/3

    =(n(n+1)(n+2)-0*1*2)/3

    =n(n+1)(n+2)/3

    (1)把n=100代入上式,得:

    1*2+2*3+3*4+···100*101

    =100*(100+1)*(100+2)/3

    =100*101*102/3

    =343400

    (3)

    n(n+1)(n+2)=(n(n+1)(n+2)(n+3)-(n-1)n(n+1)(n+2))/4

    1*2*3+2*3*4+……+n(n+1)(n+2)

    =(1*2*3*4-0*1*2*3)/4+(2*3*4*5-1*2*3*4)/4+...+(n(n+1)(n+2)(n+3)-(n-1)n(n+1)(n+2))/4

    =(n(n+1)(n+2)(n+3)-0*1*2*3)/4

    =n(n+1)(n+2)(n+3)/4

    ------若有不明白,欢迎交流

    如果明白了,毕竟是3道题!