Question

Calculati: a) (1+2+3+......+14):(1+2+3+....+6)
b) (1 x 2 x 3 x.....x15):(1+2+3+.....+15)
Va rog explicati si va multumesc daca puteti! ( va rog explicatii b )

Answer 1

a) (1+2+3+......+14):(1+2+3+....+6) =

= [14 × (14+1) : 2] : [(6 × (6+1) : 2] =

= (14 × 15 : 2) : (6 × 7 : 2) =

= (7 × 15) : (3 × 7) =

= 15 : 3 =

= 5
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b) (1 x 2 x 3 x.....x15):(1+2+3+.....+15) =

= (1 × 2 × 3 × ...× 15) : ( 15 × 16 : 2) =

= (1 × 2 × 3 × ...× 8 × .. × 15) : (15 × 8) =

( se reduc 8 × 15)

= 1 × 2 × 3 × ... × 7 × 9 × ...× 13 × 14
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