Question

10+15+20+...2010-9-13-17-...1609

Answer 1

Grupam termenii cate 2

(10 - 9 ) + (15 - 13) + (20 - 17)  +.......+ ( 2010-1609) = 1 + 2 + 3 +.......+ 401 =

dar  1+2+3+.......+ 401  este suma Gauss
care are formula de calcul S=[n(n+1)]:2=401·402/2 = 80601


10+15+20+...2010-9-13-17-...1609
S1=10+15+20+...2010
S2=9+13+17+...+1609
S1 progresie aritmetica
an=a1+(n-1)×r
2010=10+(n-1)×5     ⇒2005=5n
n=401
S1=[(a1+an)/2]×n=[10+2010)/2]×401=1010×401

an=a1+(n-1)×r
1609=9+(n-1)×5     ⇒n=401

S2=[(a1+an)/2]×n=[9+1609)/2]×401=809×401
S=[(1010-809)/2]×401
S=201×402
S=80601