大师作文网数1的3次方+2的3次方+3的3次方+4的3次方+5的3次方+..+2008的3次方的个位数是几?
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数1的3次方+2的3次方+3的3次方+4的3次方+5的3次方+..+2008的3次方的个位数是几?
n^3
= n(n+1)(n+2) - 3n(n+1) +n
= (1/4)[n(n+1)(n+2)(n+3)-(n-1)n(n+1)(n+2)] -[n(n+1)(n+2)-(n-1)n(n+1)] +(1/2)[n(n+1) -(n-1)n]
1^3+2^3+...+n^3
= (1/4)n(n+1)(n+2)(n+3) -n(n+1)(n+2)+(1/2)n(n+1)
= (1/4)n(n+1) [(n+2)(n+3)-4(n+2)+2 ]
= (1/4)n(n+1) [n^2+n]
= [(1/2)n(n+1)]^2
n=2008
1^3+2^3+...+2008^3
= [(1/2)2008(2009)]^2
=4068434225296
个位数是=6
= n(n+1)(n+2) - 3n(n+1) +n
= (1/4)[n(n+1)(n+2)(n+3)-(n-1)n(n+1)(n+2)] -[n(n+1)(n+2)-(n-1)n(n+1)] +(1/2)[n(n+1) -(n-1)n]
1^3+2^3+...+n^3
= (1/4)n(n+1)(n+2)(n+3) -n(n+1)(n+2)+(1/2)n(n+1)
= (1/4)n(n+1) [(n+2)(n+3)-4(n+2)+2 ]
= (1/4)n(n+1) [n^2+n]
= [(1/2)n(n+1)]^2
n=2008
1^3+2^3+...+2008^3
= [(1/2)2008(2009)]^2
=4068434225296
个位数是=6
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