立方的计算(要过程)1的立方+2的立方+.+N的立方=?1的立方+2的立方+.+100的立方=?2的立方+4的立方+.+
1个回答
∑n^2=∑[((n+1)^3-n^3)-3n-1]/3
=∑[(n+1)^3-n^3]/3-∑n-n/3
=[(n+1)^3-1]/3-(n+1)n/2-n/3
=n(n+1)(2n+1)/6
∑n^3=∑[((n+1)^4-n^4)-6n^2-4n-1]/4
=∑[(n+1)^4-n^4]/4-∑6n^2/4-∑n-n/4
=[(n+1)^4-1]/4-n(n+1)(2n+1)/4-n(n+1)/2-n/4
=[n(n+1)/2]^2
1^3+2^3+..+100^3=5050^2=25502500
2^3+4^3+..100^3
=(2*1)^3+(2*2)^3+(2*3)^3+..+(2*50)^3
=(2^3)*1^3+(2^3)*2^3+...+(2^3)*50^3
=8*1^3+8*2^3+...+8*50^3
=8(1^3+2^3+.+50^3)
=8*1275^2
=13005000
够详细了吧,现在知道是怎么来的了吧
相关问题
