Question

Știe cineva să rezolve acest exercițiu? Mulțumesc.​

Answer 1

$\dfrac{{}^{5)}\,3\cdot 10^n-2^n\cdot 5^{n-1}}{10^n\cdot 7} = \dfrac{3\cdot 10^n\cdot 5-2^n\cdot 5^n}{10^n\cdot 7\cdot 5} = \\ \\ = \dfrac{3\cdot 10^n\cdot 5 - (2\cdot 5)^n}{10^n\cdot 7\cdot 5} = \dfrac{10^n\cdot (3\cdot 5 - 1)}{10^n\cdot 7\cdot 5}= \\ \\ = \dfrac{3\cdot 5-1}{7\cdot 5} = \dfrac{14}{35} =\boxed{\dfrac{2}{5}}$