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![[tex] \mbox{c) } 10^{6n+2}+ 10^{3n+1}+1 \mbox{ es divisible por 111 } [/tex]](images/latex/b4d7d3217ac6a7706023fb73de84284f3f71514a_0.png "[tex] \mbox{c) } 10^{6n+2}+ 10^{3n+1}+1 \mbox{ es divisible por 111 } [/tex]")
![[tex] \mbox{ Hipoteiss inductiva }10^{6n+2}+ 10^{3n+1}+1 \mbox{ } = { } K*111 [/tex]](images/latex/f6af374e96a43c848acd3552e2a50573875aaaa6_0.png "[tex] \mbox{ Hipoteiss inductiva }10^{6n+2}+ 10^{3n+1}+1 \mbox{ } = { } K*111 [/tex]")
![[tex] \mbox{ con n+1 : } 10^{6n+8}+ 10^{3n+1}+1 [/tex]](images/latex/b0907abe14cb5743c96c9d3b07519180ecf0b64f_0.png "[tex] \mbox{ con n+1 : } 10^{6n+8}+ 10^{3n+1}+1 [/tex]")
![[tex] \mbox{a) } 3n< n^2 -1 [/tex]](images/latex/04cf715e462a402dc61690348c4daa80b22a7dd8_0.png "[tex] \mbox{a) } 3n< n^2 -1 [/tex]")
![[tex] \mbox{Hipotesis inductiva = } 3n< n^2 -1 [/tex]](images/latex/b0615c3fcb8b2ebf56f6a9c63e20e68ea585c2b9_0.png "[tex] \mbox{Hipotesis inductiva = } 3n< n^2 -1 [/tex]")
![[tex] \mbox{ Con n+1 = } 3n+3 \mbox{, por hipotesis inductiva }[/tex]](images/latex/c6c8bcd4a33aaf0c39cbee76004cb133008cd6f4_0.png "[tex] \mbox{ Con n+1 = } 3n+3 \mbox{, por hipotesis inductiva }[/tex]")
![[tex] 3n+3< n^2 -1 +3 = n^2 +2 (*) [/tex]](images/latex/613a1676983b4cb88ccdfc3ea7c13fb3ab45966a_0.png "[tex] 3n+3< n^2 -1 +3 = n^2 +2 (*) [/tex]")
![[tex] 3n+3< (n+1)^2 -1 = n^2 +2n (**) [/tex]](images/latex/0b9526eef3f050ada7b40a481e25e6b3e4b4268b_0.png "[tex] 3n+3< (n+1)^2 -1 = n^2 +2n (**) [/tex]")
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