Question

a) 2+4+6+....+500=
b) 5+10+15+....+200=
c) 1+2+3+.....+100=
d) 51+52+....+100=

Va rog ajutati.maaa este suma lui Gauuss

Answer 1

a. 2(1+2+....+250)= 2x(250x251)/2 = 62750
b. 5(1+2+...+50)=5x(50x51)/2= 6375
c. 100x101  /2= 5050
d. suma (1-100)- suma(1-50)= 5050- (50x51)/2
= 5050- 1275= 3775

sau:
a.  S = 1+ 2 + 3 +...........+(n-2) + (n-1) + n
      S= n+(n-1) +(n-2)+........... + 3 + 2 + 1 
2 S= (n-1) +(n-1) +.............(n-1) +(n-1) (suma are n termeni) 
2S=n (n+1) 
S= n(n+1):2