0..1..4..9..16..25...求这个数列的第一项到第n项的求和,

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0..1..4..9..16..25...求这个数列的第一项到第n项的求和,
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0..1..4..9..16..25...求这个数列的第一项到第n项的求和,
0..1..4..9..16..25...求这个数列的第一项到第n项的求和,

0..1..4..9..16..25...求这个数列的第一项到第n项的求和,
因为an=(n-1)²
Sn=0+1+2²+3²+.+(n-1)²
又n³=(n-1+1)³=(n-1)³+3(n-1)²+3(n-1)+1
所以n³-(n-1)³=3(n-1)²+3(n-1)+1
即:
1³-0³=3*0²+3*0+1
2³-1³=3*1²+3*1+1
3³-2³=3*2²+3*2+1
.
n³-(n-1)³=3(n-1)²+3(n-1)+1
把以上各式累加得:
n³-0³=3[0²+1²+2²+.+(n-1)²]+3[1+2+3+.(n-1)]+n
即n³=3Sn+(3/2)n(n-1)+n
所以Sn=(2n³-3n²+n)/6=n(n-1)(2n-1)/6

36..49..64..81..0+1=1+3=4+5=9+7=16+9=25+11=36+13=49以此类推,每过一项多加2

规律an=(n-1)²

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