Considere a seguinte sequência begin display style open parentheses negative 1 comma 0 comma 1 half comma 3 over 4 comma 7 over 8 comma 15 over 16 comma 31 over 32 comma... close parentheses end style. Assinale a alternativa que corresponde à definição dessa sequência recursivamente.
a.
begin display style x subscript 1 equals negative 1 end style, begin display style x subscript n equals x subscript n minus 1 end subscript over 2 plus 1 over 2 to the power of n minus 1 end exponent end style.
b.
begin display style x subscript n equals fraction numerator 2 to the power of n minus 1 over denominator 2 to the power of n end fraction end style.
c.
begin display style x subscript 1 equals 1 end style, begin display style x subscript n equals x subscript n minus 1 end subscript over 2 end style.
d.
begin display style x subscript 1 equals 0 end style, begin display style x subscript n equals x subscript n minus 1 end subscript over 2 plus 1 half end style.
e.
begin display style x subscript 1 equals negative 1 end style, x subscript n equals x subscript n minus 1 end subscript over 2 plus 1 half.