Question

vă rog ajutati-mă vă dau coroana

Answer 1

Cerinta:  Simplificati fractiile !

Răspuns

Explicație pas cu pas:

b)

( 5ⁿ⁺¹ + 8 x 5ⁿ ) / ( 3ⁿ + 3ⁿ⁺¹ + 3ⁿ⁺² ) =

= ( 5ⁿ x 5 + 5ⁿ x 8 ) / ( 3ⁿ + 3ⁿ x 3 + 3ⁿ x 3² ) =

= 5ⁿ ( 5 + 8 ) / 3ⁿ ( 1 + 3 + 3² ) =

= ( 5ⁿ x 13 ) / ( 3ⁿ x 13 ) = →  simplific cu 13

= 5ⁿ / 3ⁿ =

= ( 5 / 3 )ⁿ

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c)

( 2 + 4 + 6 + ....... + 160 ) / ( 3 + 6 + 9 + ...... + 240 ) = 2 / 3

= 2 ( 1 + 2 + 3 + ...... + 80 ) / 3 ( 1 + 2 + 3 + ..... + 80 ) =

        → simplific sumele

= 2 / 3

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sau calculez sumele

2 ( 1 + 2 + 3 + ...... + 80 ) / 3 ( 1 + 2 + 3 + ....... + 80 ) =

= [ 2 × 80 × ( 1 + 80 ) : 2 ] / ( 3 × 80 × 81 : 2) =

= ( 80 × 81 ) / ( 3 × 40 × 81 ) = → simplific cu 81

= ( 2 x 40 ) / ( 3 x 40 ) = → simplific cu 40

= 2 / 3