Question

1.Determinati n∈N, astfel incat fractia $\frac{2n+7}{3n+1} ,$ ,sa fie echiunitara.
2.Determinati n∈N, astfel incat fractia$\frac{1+2+2^{2}+...+ 2^{100} }{2n}$ sa fie subunitara.Dau coronita!

Answer 1

 [tex]2).\;\;1+2+2^2+...+2^{100}=2^{101}-1\;\rightarrow\;fractia\;este\;subunitara \\daca:\;2^{101}-1\ \textless \ 2^n\;adica:\;\;2^{101}\,\ \textless \ \,2^n+1\;;\;n\le101.\\ 1).\;\rightarrow\;2n+7=3n+1\Leftrightarrow\;3n-2n=7-1\;;\;n=6\;; [/tex]