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1²+2²+3²+...+n² = Sn
1 5 14 30 55 91
6²
36
5²
25
4²
16
3²
9
2²
4
1²
1
Sn = n³/3 +n²/2 +n/6 bella da vedere
= n(2n²+3n+1)/6 comoda da calcolare
S0= 0+ 0 +0
S1= 1/3+1/2+1/6 = 2/6+3/6+1/6 = 6/6 = 1
S2= 2*(2*4+3*2+1)/6 = 2*15/6 = 5
S3= 3*(2*9+3*3+1)/6 = 3*28/6 = 14
S4= 4*(2*16+3*4+1)/6 = 4(32+12+1)/6 = 30
Formula, e verifica in alcuni casi.