Question

calculati suma s=1+3+5+...+95+97+99:

Answer 1

s=1+3+5+...+95+97+99 e de forma 1+3+5+..+2n-1=

99=2n-1 unde

2n=99+1

2n=100

n=100:2

n=50

Suma este egala cu 50x50=2500

Answer 2

S = 1 + 3 + 5 + ....... + 95 + 97 + 99

→ suma are 50 de termeni ( suma primelor 50 de numere impare consecutive)

( 99 - 1 ) : 2 + 1 = 98 : 2 + 1 = 49 + 1 = 50 termeni

sau ( 99 + 1 ) : 2 = 100 : 2 = 50  

→ aplic formula sumei lui Gauss

S = 50 × ( 1 + 99 ) / 2

S = 25 × 100

S = 2 500