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5^n+2*7^n+5^n*7^n+1 /5^n+1*7^n+1+7^n*5^n+2

Răspuns :


(5^n+2*7^n+5^n*7^n+1) / (5^n+1*7^n+1+7^n*5^n+2) =

= (5²·5ⁿ·7ⁿ + 5ⁿ·7ⁿ ·7) / (5·5ⁿ·7ⁿ·7 + 5ⁿ·7ⁿ·5²) =

(25·35ⁿ + 35ⁿ·7)/(35·35ⁿ + 35ⁿ·25) = [35ⁿ(25+7)][35ⁿ(35+25)] = 32/60 = 8/15