Question

Calculeaza sumele: a. 11+22+33+44+.............+440 b.30+60+90+120+................+720. Cu explicatie.

Answer 1

a) 11+22+33 + 44 + ...+ 440=9020
dam factor comun pe 11
11( 1+2+3+4+...+40)=
1+2+3+4+...+40= (40x(40+1)):2= (40x41):2=1640:2=820
11 + 22+33+44+...+440 = 11 x820= 9020

b) 30+60+90+120+...+720 = 9000
dam factor comun pe 30
30( 1+2+3+4+...+ 24)= 30 x300 = 9000
1+2+3+4+...+24=(24x(24+1)):2= (24x25):2= 600:2=300

Answer 2

a) 11 + 22 + 33 + 44 + ........ + 440 =  → il dau factor comun pe 11
= 11 × ( 1 + 2 + 3 + 4 + .......+ 40 ) = 
= 11 x [ 40 x (1 + 40) : 2]=
                     ↓
                  aplic formula:  ,,suma lui Gauss"
= 11 x ( 20 x 41) = 
= 11 x 820=
= 9 020 

b) 30 + 60 + 90 + ........ + 720 = 9 000
= 30 × ( 1 + 2 + 3 + .........+ 24) = 
= 30 × [ 24 × ( 1 + 24) : 2 ]=
= 30 × ( 12 ×25) = 
= 30 × 300 =
= 9 000