2×2+4×4+6×6……100×100

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|2^2+4^2+6^2+……+(2n-2)^2 |
|=(2*1)^2+(2*2)^2+(2*3)^2+....+[2*(n-1)]^2 |
|=2^2*{1^2+2^2+3^2+……+(n-1)^2} |
|=4*(n-1)n(2n-1)/6. |
|令n=51 |
|4*(n-1)n(2n-1)/6. |
|=171700 |
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(2^2+4^2+......+100^2) - (1^2+3^2+ ......+99^2)
= [(1+1)^2+(3+1)^2+......+(99+1)^2] - (1^2+3^2+ ......+99^2)
= 1*2+1+3*2+1+.......+99*2+1
=(1+3+5+.......+99)*2 +1*50
=5050

用一般数列求和的方法。
1^2+2^2+3^2+..........+n^2=n/6(n+1)(2n+1)