Respuesta :

jorgezarate

Answer:

  • It is true for  n=1
  • if n=k is true then n=k+1 is also true

Step-by-step explanation:

  • n=1:

[tex]1=1(3*1-1)/2\\1=2/2\\1=1\\[/tex]       TRUE

  • n=k:

[tex]1 + 4 +7 + ...+(3k -2) = k (3k - 1)/2\\[/tex]

  • n=k+1:

[tex]1 + 4 +7 + ...+(3k -2)+ (3(k+1)-2) =k(3(k+1)-1)/2 \\[/tex]

We replace the first part of the equation with our value for n=k:

[tex]k (3k - 1)/2+(3(k+1)-2)=k(3(k+1)-1)/2 \\[/tex]

we develop both sides of the equation to verify equality:

[tex]3k^{2} /2-k/2+3k+1=(k+1)(3k+2)/2\\\\3k^{2} /2+5k/2+1=(3k^{2}+5k+2)/2\\\\3k^{2} /2+5k/2+1=3k^{2} /2+5k/2+1[/tex]       TRUE

Otras preguntas