Răspuns:
Explicație pas cu pas:
( 1 + 3 + 5 + ..... + 99 ) / ( 2 + 4 + 6 + ..... + 200 ) = 25 / 101
= [ ( 99 - 1 ) : 2 + 1 ] × ( 1 + 99 ) : 2 / 2 × ( 1 + 2 + 3 + ..... + 100 ) =
= ( 50 × 100 : 2 ) / 2 × ( 100 × 101 ) : 2 =
= 50² / 10100 =
= 2500 / 10100 =
= 25 / 101
_________________________________________
1 + 3 + 5 + ..... + 99 = 2 500
→ stabilesc cati termeni are suma numerelor impare
( 99 - 1 ) : 2 + 1 = 98 : 2 + 1 = 50 termeni are suma , ce reprezinta numaratorul fractiei
→ aplic formula sumei lui Gauss
= 50 × ( 1 + 99 ) : 2 =
= 5000 : 2 =
= 2 500
____________________________________
iar la numitor am dat factor comun pe 2
