230问答网 > 1）1x2+2x3+3x4+...+100x101= 2）1x2+2x3+3x4+...n(n+1)= （3）1x2x3+2x3x4+3x4x5+...+n（n+1)（n+2）=

1）1x2+2x3+3x4+...+100x101= 2）1x2+2x3+3x4+...n(n+1)= （3）1x2x3+2x3x4+3x4x5+...+n（n+1)（n+2）=

2025-01-03 06:47:33

推荐回答（2个）

回答1：

(1)1x2+2x3+3x4+...+100x101
=1/3*(100*101*102-99*100*101+99*100*101......-0*1*2)
=1/3*102*100*101
=343400

(2)1x2+2x3+3x4+...n(n+1)=
=1/3*[n*(n+1)*(n+2)-(n-1)*n*(n+1)......-0*1*2]
=1/3n(n+1)(n+2)

(3)1x2x3+2x3x4+3x4x5+...+n(n+1)(n+2)
=1/4[n(n+1)(n+2)(n+3)-(n-1)n(n+1)(n+2)+(n-1)n(n+1)(n+2).....-0*1*2*3)]
=1/4n(n+1)(n+2)(n+3)

回答2：

(1)1/3(100x101x102)

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

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