Question

Determinati numarul natural n , pentru care sunt adevarate egalitatile: 2 la puterea 1+2+3+...+12=2 la puterea n+3

Answer 1

 [tex]Dac\u{a}\;inteleg\;bine\;avem:\; 2^{1+2+3+...+12}=2^{n+3}\\ 1+2+3+...+12=\frac{12\cdot13}{2}=6\cdot13=78=75+3\\ \Rightarrow\;2^{75+3}=2^{n+3}\;\Leftrightarrow\;\;\fbox{n=75}[/tex]

Answer 2

1+2+3+...+12=12x13:2=78
Deci 2⁷⁸=2 la n x2³
2 la puterea n=2⁷⁸:2³
2 la puterea n=2⁷⁵⇒n=75