Question

2×2×2+4×4×4+6×6×6+…+98×98×98+100×100×100 简便计算~

Answer 1

设2×2×2为a

原式=a+8a+27a+…

=1³a＋2³a＋3³a+...+49³a＋50³a

=(1+2+3+...+50)²a

=1275²a

=1625625×(2×2×2)

=13005000

=1³a＋2³a＋3³a+...+49³a＋50³a

=(1+2+3+...+50)²a推倒如下

1*1*1+2*2*2

=9

=3*3

=1×1×1+2×2×2+3×3×3

=36

=6*6

=(1+2+3)×(1+2+3)

所以可以的到结论如下:

1×1×*1+2×2×2+3×3×3+...+x×x×x

=(1+2+3+...+x)×(1+2+3+...x)