REPEDE VA ROG 12 PUNCTE
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Răspuns: n = 1
Explicație pas cu pas:
Salutare !
[tex]\bf 2^{n+5} + 2^{n+4} + 2^{n+3} + 2^{n+2} + 2^{n+1} = 124[/tex]
[tex]\bf 2^{n+1} \cdot(2^{n+5-(n+1)} + 2^{n+4-(n+1)} + 2^{n+3-(n+1)} + 2^{n+2-(n+1)} + 2^{n+1-(n+1)}) = 124[/tex]
[tex]\bf 2^{n+1} \cdot(2^{4} + 2^{3} + 2^{2} + 2^{1} + 2^{0}) = 124[/tex]
[tex]\bf 2^{n+1} \cdot(16 + 8+4+2+1) = 124[/tex]
[tex]\bf 2^{n+1} \cdot 31 = 124\:\:\Big|:31[/tex]
[tex]\bf 2^{n+1} = 4[/tex]
[tex]\bf 2^{n+1} = 2^{2}\implies n+1 = 2 \implies n = 2-1\implies \boxed{\bf n= 1}[/tex] ∈ IN
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