Question

1.Calculati suma nr nat care impartite la 485 dau catul 6.
2.Aflati suma nr cae impartite la 23 dau catul 9.

Answer 1

1.  n = 485·6 + r    r < 485      r ∈ {0,1,2,3........484}
n = 2910 + r
S = 2910 + (2910 + 1) + (2910 + 2) +.....................+ (2910 + 484)
S = 2910·485 + ( 1 + 2 + 3 +.......+ 484) = 2910·485 + 484·485/2
S = 485(2910 + 242) = 485·3152
2.  n = 23·9 + r = 207 + r    r < 23    r ∈ { 0,1,2,3.......22}
S = 207 + (207+1) + (207 + 2) +........+ (207 + 22)
S = 207·23 + 22·23/2 = 23(207 + 11) = 23·218