Considere a prova do seguinte teorema, utilizando o Princípio da Indução Finita: Para todo n element of straight natural numbers, 2 plus 5 plus 8 plus... plus left parenthesis 2 plus 3 n right parenthesis equals fraction numerator left parenthesis n plus 1 right parenthesis left parenthesis 4 plus 3 n right parenthesis over denominator 2 end fraction. Assinale a alternativa que corresponde à hipótese de indução. a. Fixado k element of straight natural numbers, 2 plus 5 plus 8 plus... plus left parenthesis 2 plus 3 k right parenthesis equals fraction numerator 3 k over denominator 2 end fraction. b. Fixado k element of straight natural numbers, 2 plus 5 plus 8 plus... plus left parenthesis 2 plus 3 left parenthesis k plus 1 right parenthesis right parenthesis equals fraction numerator left parenthesis k plus 2 right parenthesis left parenthesis 4 plus 3 left parenthesis k plus 1 right parenthesis right parenthesis over denominator 2 end fraction. c. Fixado k element of straight natural numbers, 2 plus 5 plus 8 plus... plus left parenthesis 2 plus 3 k right parenthesis equals fraction numerator left parenthesis k plus 1 right parenthesis left parenthesis 4 plus 3 k right parenthesis over denominator 2 end fraction. d. 2 plus 5 equals fraction numerator left parenthesis 1 plus 1 right parenthesis left parenthesis 4 plus 3.1 right parenthesis over denominator 2 end fraction. e. Fixado k element of straight natural numbers, 2 plus 5 plus 8 plus... plus left parenthesis 2 plus 3 k right parenthesis equals fraction numerator k left parenthesis 4 plus 3 k right parenthesis over denominator 2 end fraction.
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