Question

3×3×3+4×4×4+5×5×5+6×6×6+7×7×7

3×3×3+4×4×4+5×5×5+6×6×6+7×7×7
=???????????????????
=???????????
=???

Answer 1

首先,有一个公式,(a+b)^3=a^3+ 3(a^2)b + 3a(b^2)+b^3
(a-b)^3=a^3- 3(a^2)b + 3a(b^2)-b^3
则,(a+b)^3 +(a-b)^3 =2*(a^3) + 6a(b^2)

3×3×3+4×4×4+5×5×5+6×6×6+7×7×7
= (5-2)^3 + (5-1)^3 +5^3 + (5+1)^3 + (5+2)^3
= 2*5^3 + 6*5*4 +5^3 + 2*5^3 + 6*5*1
= 775

放在这里用固然有点小题大做，但是这种方法即使有100项，也一样做的。
n^2的前n项和也有个公式……不过你现在大概还用不到de……

Answer 2

27+64+125+216+343=775

Answer 3

立方和公式
1^3+2^3+......n^3=[n(n+1)/2]^2
3×3×3+4×4×4+5×5×5+6×6×6+7×7×7 =[7*(7+1)/2]^2-2^3-1=784-9=775

Answer 4

3×3×3+4×4×4+5×5×5+6×6×6+7×7×7
=27+64+125+343+216
=216+343+216
=775

Answer 5

3×3×3+4×4×4+5×5×5+6×6×6+7×7×7

=27+64+125+216+343

=775

Answer 6

3×3×3+4×4×4+5×5×5+6×6×6+7×7×7
=27+64+125+216+343
=370+280+125
=775