Pertanyaan

Sederhanakanlah: a. 4 n 4 n + 1 − 2 2 n + 1

Sederhanakanlah:

a. $\frac{4 ^{n + 1} - 2 ^{2 n + 1}}{4 ^{n}}$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

hasil dari adalah .

hasil dari $fraction numerator 4 to the power of n plus 1 end exponent minus 2 to the power of 2 n plus 1 end exponent over denominator 4 to the power of n end fraction$ adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table

table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table

Pembahasan

Ingat kembali: Pertama mengubah menjadi bilangan berpangkat sebagai berikut. Kemudian, diperoleh perhitungan: Jadi, hasil dari adalah .

Ingat kembali:

a to the power of n equals stack stack a cross times a cross times a cross times... cross times a with underbrace below with a space s e b a n y a k space n below comma space a not equal to 0

a to the power of m times a to the power of n equals a to the power of m plus n end exponent. space a not equal to 0

left parenthesis a to the power of m right parenthesis to the power of n equals a to the power of m times n end exponent

Pertama mengubah menjadi bilangan berpangkat sebagai berikut.

4 equals 2 cross times 2 equals 2 squared

Kemudian, diperoleh perhitungan:

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

Jadi, hasil dari $fraction numerator 4 to the power of n plus 1 end exponent minus 2 to the power of 2 n plus 1 end exponent over denominator 4 to the power of n end fraction$ adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table .

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