База
[tex]4^1=4 > 7-5=2\\4^2=16 > 14-5=9[/tex]
Пусть
[tex]4^n > 7n-5,\quad n \geq 2[/tex]
Тогда
[tex]4^{n+1}=4\cdot4^n > 4(7n-5) = 28n-20 = 7(n+1)-5+21n-22 > 7(n+1)-5[/tex]
при [tex]n \geq 2[/tex]
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Verified answer
База
[tex]4^1=4 > 7-5=2\\4^2=16 > 14-5=9[/tex]
Пусть
[tex]4^n > 7n-5,\quad n \geq 2[/tex]
Тогда
[tex]4^{n+1}=4\cdot4^n > 4(7n-5) = 28n-20 = 7(n+1)-5+21n-22 > 7(n+1)-5[/tex]
при [tex]n \geq 2[/tex]