Corectie: ( 5ⁿ⁺¹ + 8 x 5ⁿ) NU = 5ⁿ
Răspuns
Explicație pas cu pas:
( 5ⁿ⁺¹ + 8 x 5ⁿ ) / ( 3ⁿ + 3ⁿ⁺¹ + 3ⁿ⁺² ) =
= ( 5ⁿ x 5 + 8 x 5ⁿ ) / ( 3ⁿ + 3ⁿ x 3 + 3ⁿ x 3² ) =
= [ 5ⁿ x ( 5 + 8 ) ] / [ 3ⁿ x ( 1 + 3 + 3² ) ] =
= ( 5ⁿ x 13 ) / ( 3ⁿ x 13 ) = => simplificam prin 13
= 5ⁿ / 3ⁿ =
= ( 5 / 3 )ⁿ
_______________________________________
b)
( 2 + 4 + 6 + ..... + 160 ) / ( 3 + 6 + 9 + ...... + 240 ) = 2 / 3
= 2 ( 1 + 2 + 3 + .... + 80 ) / 3 ( 1 + 2 + 3 + ..... + 80 ) =
==> simplific sumele
= 2 / 3
_______________
sau calculand sumele:
2 ( 1 + 2 + 3 + ..... + 80 ) = 2 × 80 × 81 / 2 = 2 × 3 240
3 ( 1 + 2 + 3 + ...... + 80 ) = 3 × 80 × 81 / 2 = 3 × 3 240
_______________________________________
( 2 × 3 240 ) / ( 3 × 3 240 ) = 2 / 3 → simplific cu 3 240
