å
¬å¼ï¼1^2+2^2+3^2+...+n^2=n(n+1)(2n+1)/6
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æ们ç¥é(m+1)^3-m^3=3m^2+3m+1ï¼å¯ä»¥å¾å°ä¸åçå¼ï¼
2^3 - 1^3 = 3*1^2 + 3*1 + 1
3^3 - 2^3 = 3*2^2 + 3*2 + 1
4^3 - 3^3 = 3*3^2 + 3*3 + 1
.........
(n+1)^3 - n^3 = 3.n^2 + 3*n + 1
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(n+1)^3 - 1 = 3*Sn + 3*n(n+1)/2 + n
å
¶ä¸Sn = 1^2 + 2^2 + 3^2 + ...... + n^2
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Sn = n*(n + 1)*(2n + 1)/6
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