wmutex

Pentru problema bonus:

N = [radical ( suma[i=1..23] i(i+1)(i+2) ) / 10] =
[radical ( suma[i=1..23] i³ +3i² + 2i ) / 10] =
[radical ( suma[i=1..23] i³ +3suma[i=1..23] i² + 2suma[i=1..23] i ) / 10]

Dat find ca:

suma[i=1..n] i³ = n²(n+1)²/4
suma[i=1..n] i² = n(n+1)(2n+1)/6
suma[i=1..n] i = n(n+1)/2

rezulta

suma[i=1..n] i³ +3suma[i=1..n] i² + 2suma[i=1..n] i = n(n+1)(n+2)(n+3)/4

deci, pentru n=23:

N = [radical(23 x 24 x 25 x 26 / 4) / 10] = [radical(23 x 6 x 25 x 26 / 100)] = [radical(897)]

Avem:

29² = 841 < 897 < 900 = 30²

deci:

N = [radical(897)] = 29.

Adica exact varsta persoanei care a propus problema. Oare de ce nu m-am gandit la asta din prima?... scuteam o gramada de calcul. :-)