1x1x1+2x2x2+3x3x3+4x4x4+．．．+100x100x100=?
thx
1x1x1+2x2x2+3x3x3+4x4x4+．．．+100x100x100=?
2007-05-13 1:00 am
回答 (6)
2007-05-13 6:21 pm
✔ 最佳答案
30251×1×1＝1
1×1×1＋2×2×2＝9＝3×3＝(1＋2)×(1＋2)
1×1×1＋2×2×2＋3×3×3＝36＝6×6＝(1＋2＋3)×(1＋2＋3)
1×1×1＋2×2×2＋3×3×3＋4×4×4＝100＝10×10＝(1＋2＋3＋4)×(1＋2＋3＋4)
所以，依規律，1×1×1＋2×2×2＋3×3×3＋…＋100×100×100＝(1＋2＋3＋4＋5＋6＋7＋8＋9＋10)×(1＋2＋3＋4＋5＋6＋7＋8＋9＋10)＝55×55＝3025
2007-05-25 2:23 am
點解條式全部都係加但係answer細過100x100x100(1'000'000)??
2007-05-15 4:10 am
1x1x1+2x2x2+3x3x3+4x4x4+．．．+100x100x100
=25502500
用公式
<[n(n+1]÷2>^2
=25502500
用公式
<[n(n+1]÷2>^2
2007-05-14 12:04 am
' 1x1x1+2x2x2+3x3x3+4x4x4+．．．+100x100x100
'=1^3+2^3+3^3+4^3+.................+100^3
'=(1+2+3+4+...............+100)^3
'=5050^3
'=128787625000
'=1^3+2^3+3^3+4^3+.................+100^3
'=(1+2+3+4+...............+100)^3
'=5050^3
'=128787625000
2007-05-13 1:05 am
(100 * 101 / 2 )^2 = 25502500
用公式計...好快手
用公式計...好快手
收錄日期: 2021-04-12 19:32:41
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20070512000051KK03408