Question

Calculați următoarele sume:
a) 1 + 2 +3 + ... + 80;
c) 1 + 3 + 5 + ... +99;
b) 2 + 4 + 6 + ... + 100;
d) 3+7+ 11 + 15 + ... + 43.​

Answer 1

a) 1+2+3+... +80 =

= [80·(80+1)]/2

= (80·81)/2

= 40·81

= 3240

b) 2+4+6+...+100 =

= 2·(1+2+3+...+50)

= 2·[50·(50+1)]/2

= 50·(50+1)

= 50·51

= 2550

c) 1+3+5+...+99 =

= 1+3+5+...+(2·50-1)

= 50²

= 2500

d) 3+7+11+15+...+43 =

= (4·1-1)+(4·2-1)+(4·3-1)+...+(4·11-1)

= 4·(1+2+3+...+11) -1-1-1-...-1 {de 11 ori}

= 4·[11·(11+1)]/2 - 11

= 4·(11·12)/2 - 11

= 4·11·6 - 11

= 11·(24-1)

= 11·23

= 253