Question

Calculati:
a). 36+37+38+...+78+79 b). 2+4+6+...48+50 c). 1+2+3+...29+30
Va rog ajutatima! Maine am mate!!!!!

Answer 1

a)36+37+38+...+78+79
se adauga (1+2+3+....+35)+36+37+38+...+78+79 ⇒S=1+2+3+....+79 care este
Suma Gauss cu formula de calcul S=[n(n+1)]:2 ⇒S1=(79×80):2
S2=(1+2+3+....+35)=(35×36):2=630
S=S1-S2= (79×80):2-(35×36):2=3160
S=3160-630=2530

36+37+38+...+78+79 =2530

sau metoda 2

36+37+38+...+78+79
=progresie aritmetica
a1=36, ratia=1 si an=79
an=a1+(n-1)×r
79=36+(n-1)×1
79-36=n-1
n=44
S=[(a1+an)×n]:2=[(36+79)×44]:2=2530

b)
2+4+6+...48+50=2(1+2+3+.....25)
(1+2+3+.....25)=Suma Gauss cu formula de calcul S=[n(n+1)]:2

S = [n(n+1)]:2 = (25×26) : 2 = 325

2 + 4 + 6 +...48 + 50 = 2( 1 + 2 + 3+.....25) = 2 × 325 = 650

c)
1 + 2 + 3 +...29 + 30 = (30 × 31):2 = 465