Question

Aflati suma numerelor care impartite la 43 dau catul 15 si restul numar par.

Answer 1

n = 43·15 + r    r < 43, nr. par ⇒ r∈{2,4,6,8,10,1,2,14,16,......42}  (21 valori)
S = (645 + 1·2) +(645 + 2·2) +(645+3·2) +..........+ (645+21·2)
S = 645·21 + 2( 1+2+3+.....+21) = 645·21 + 2·21·22/2 = 21(645+ 22)
S = 21·667 = 14007

Answer 2

n=43 x 15 +r=645+r
r={0; 2 ; 4; 6............42} r<43
n={645; 647; 649; ...............687}
S=645+647+649+.........+687=(645+687)[(687-645)/2+1]/2=1332 x 21/2
S=13986