Question

n²+(n-1)²+(n-2)²+(n-3)²+......(n-n)²的结果,很急

Answer 1

n²+(n-1)²+(n-2)²+(n-3)²+......+(n-n)²
当n=1时，n²+(n-1)²+(n-2)²+(n-3)²+......+(n-n)²
=1²+(1-1)²
=1+0
=1
当n=2时，n²+(n-1)²+(n-2)²+(n-3)²+......+(n-n)²
=2²+(2-1)²+(2-2)²
=4+1+0
=5
当n=3时，n²+(n-1)²+(n-2)²+(n-3)²+......+(n-n)²
=3²+(3-1)²+(3-2)²+(3-3)²
=9+4+1+0
=14
......
所以，n²+(n-1)²+(n-2)²+(n-3)²+......+(n-n)²
=n*(n+1)*(2n+1)/6

Answer 2

n*n^2-(2n+4n+6n+......+2n^2)+(1+1+4+9+......+n^2)