Question

Determinat:
a) S = 1+2+3....+44
b) S = 1+2+3....+98
c) S = 1+2+3....+85
d) S = 1+2+3....+2014
Va rod ajutatima !! 

Answer 1

a) S = 1+2+2+...+44
    S= 44+43+42+...+1 
  S+S = 45+45+45+...+45 si sunt 44-1+1 = 44 termeni 
 2 * S = 45* 44
 2* S = 1980
S= 1980 : 2
S= 990
b)S=1+2+3+...+98 ( aplicam direct suma lui Gauss)
S=98*99/2
S=49*99
S=4851
c)S=1+2+3+...+85
S=85*86/2
S=85*43
S=3655
d)S=1+2+3++...+2014
S=2014*2015/2
S=1007*2015
S=2029105
Sper ca te-am ajutat !