Question

Va rog mult azi dau teza la matematica Cum calculez suma lui Gauss in urmatoarele ecemple 1+2+3+4+5.......+70 b)2+4+6+8.........+80 c)1+3+5+7+8.......+50va implor

Answer 1

a) 1+2+3+4+5.......+70
Suma Gauss are formula de calcul S=[n(n+1)]:2
S=[70×(70+1)]:2=2485
b)
2+4+6+8+....+80=2(1+2+3+4+....40)=2×[40(40+1)]:2=1640

c)
1+3+5+7+8.......+50

Formula lui Gauss pentru sume de numere impare (suma incepe cu numarul 1)

1 + 3 + 5 + 7 + … + ( 2n – 1 ) = n x n

2n-1=50⇒2n=51⇒n=51/2

1+3+5+7+8.......+50=51/2×51/2=2601/4

Answer 2

1+2+3...+70=2455 ;2+4+6....+80=1640 ; 1+3+5+7+9....+49=625 la ultimu sunt calculate din 2 in 2 nr impare si merg pana la 49