Pertanyaan

2 n − 2 n + 1 2 n + 2 − 2 n + 1 = ...

$\frac{2 ^{n + 2} - 2 ^{n + 1}}{2 ^{n} - 2 ^{n + 1}} = ...$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Ingat! 1. Faktorisasi menggunakan hukum distributif 2. Sifat bilangan berpangkat: Maka: Oleh karena itu, jawaban yang tepat adalah E.

Ingat!

1. Faktorisasi menggunakan hukum distributif

2. Sifat bilangan berpangkat:

Maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 to the power of n plus 2 end exponent minus 2 to the power of n plus 1 end exponent over denominator 2 to the power of n minus 2 to the power of n plus 1 end exponent end fraction end cell equals cell fraction numerator 2 to the power of n cross times 2 squared minus 2 to the power of n cross times 2 to the power of 1 over denominator 2 to the power of n minus 2 to the power of n cross times 2 to the power of 1 end fraction end cell row blank equals cell fraction numerator 2 to the power of n open parentheses 2 squared minus 2 to the power of 1 close parentheses over denominator 2 to the power of n open parentheses 1 minus 2 to the power of 1 close parentheses end fraction end cell row blank equals cell fraction numerator 2 to the power of n open parentheses 4 minus 2 close parentheses over denominator 2 to the power of n open parentheses 1 minus 2 close parentheses end fraction end cell row blank equals cell fraction numerator 2 to the power of n cross times 2 over denominator 2 to the power of n cross times open parentheses negative 1 close parentheses end fraction end cell row blank equals cell 2 to the power of n over 2 to the power of n cross times fraction numerator 2 over denominator open parentheses negative 1 close parentheses end fraction end cell row blank equals cell 2 to the power of n minus n end exponent cross times open parentheses negative 2 close parentheses end cell row blank equals cell 2 to the power of 0 cross times open parentheses negative 2 close parentheses end cell row blank equals cell 1 cross times open parentheses negative 2 close parentheses end cell row blank equals cell negative 2 end cell end table$

Oleh karena itu, jawaban yang tepat adalah E.