Question

Calculati a-b+c unde: a= 1+2+3+...+458, b= 168+169+170+...+192, c= 15+16+17+...+52

Answer 1

a=1+2+3+...+458
a=458*459/2
a=105111

b=168+169+170+...+192  Facem un artificiu

1+2+....167+168+169+...+192 - (1+2+...+167)
192*193/2   -   167*168/2 = 
18528 - 14028 = 
4500

c=15+16+17+...+52  La fel, adunam 1+2+3 +...+14 si pe urma ii scadem 
1+2+3+...+14+15+16+....+52 - (1+2+3+...+14) = 
52*53 / 2- 14*15/2 = 
1378-105=
1273

iar a-b+c = 
105111 - 4500 + 1273 = 101884