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)=⑶1*2*3+2*3*4+……+n(n+1)(n+2)=
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![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)=⑶1*2*3+2*3*4+……+n(n+1)(n+2)=](/uploads/image/z/2740204-28-4.jpg?t=%E7%8E%B0%E5%9C%A8%E6%80%A5%E9%9C%80%E7%9A%84%E6%95%B0%E5%AD%A6%E8%AE%A1%E7%AE%97%7E%7E%7E%E2%91%B41%2A2%2B2%2A3%2B3%2A4%2B%E2%80%A6%E2%80%A6%2B100%2A101%3D%E2%91%B51%2A2%2B2%2A3%2B3%2A4%2B%E2%80%A6%E2%80%A6%2Bn%28n%2B1%29%3D%E2%91%B61%2A2%2A3%2B2%2A3%2A4%2B%E2%80%A6%E2%80%A6%2Bn%28n%2B1%29%28n%2B2%29%3D)
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)=⑶1*2*3+2*3*4+……+n(n+1)(n+2)=
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)=
⑶1*2*3+2*3*4+……+n(n+1)(n+2)=
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)=⑶1*2*3+2*3*4+……+n(n+1)(n+2)=
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!
(1)1*2+2*3+3*4+···100*101
=1^2+1+2^2+2+3^2+3+···+100^2+100
=1^2+2^2+···+100^2+1+2+···+100
利用下面公式
1^2+2^2+3^2+……+n^2=n(n+1)(2n+1)/6
1+2+3+···+n=n(n+1)/2
在上式中,n=100,代入得,
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(1)1*2+2*3+3*4+···100*101
=1^2+1+2^2+2+3^2+3+···+100^2+100
=1^2+2^2+···+100^2+1+2+···+100
利用下面公式
1^2+2^2+3^2+……+n^2=n(n+1)(2n+1)/6
1+2+3+···+n=n(n+1)/2
在上式中,n=100,代入得,
1*2+2*3+3*4+···100*101=100*101*201/6+100*101/2=343400
(2)
原式=1^2+2^2+3^2+......+n^2+1+2+3+...+n
=n*(n+1)(2n+1)/6+n*(1+n)/2
(3)不会
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