(1/(2^n)+-1/(2^(2n)))^2

 Esercizio

$\left(\frac{1}{2^n}-\frac{1}{2^{2n}}\right)^2$

 

Applicare la formula: $\left(a+b\right)^2$$=a^2+2ab+b^2$, dove $a=\frac{1}{2^n}$, $b=\frac{-1}{2^{2n}}$ e $a+b=\frac{1}{2^n}+\frac{-1}{2^{2n}}$

$\left(\frac{1}{2^n}\right)^2+\frac{-2}{2^{2n}2^n}+\left(\frac{-1}{2^{2n}}\right)^2$

 

Applicare la formula: $x^mx^n$$=x^{\left(m+n\right)}$, dove $x=2$ e $m=2n$

$\left(\frac{1}{2^n}\right)^2+\frac{-2}{2^{\left(2n+n\right)}}+\left(\frac{-1}{2^{2n}}\right)^2$

 

Combinazione di termini simili $2n$ e $n$

$\left(\frac{1}{2^n}\right)^2+\frac{-2}{2^{3n}}+\left(\frac{-1}{2^{2n}}\right)^2$

 

Applicare la formula: $\left(\frac{a}{b}\right)^n$$=\frac{a^n}{b^n}$, dove $a=1$, $b=2^n$ e $n=2$

$\frac{1}{2^{2n}}+\frac{-2}{2^{3n}}+\left(\frac{-1}{2^{2n}}\right)^2$

 

Applicare la formula: $\left(\frac{a}{b}\right)^n$$=\frac{a^n}{b^n}$, dove $a=-1$, $b=2^{2n}$ e $n=2$

$\frac{1}{2^{2n}}+\frac{-2}{2^{3n}}+\frac{1}{2^{4n}}$

$\frac{1}{2^{2n}}+\frac{-2}{2^{3n}}+\frac{1}{2^{4n}}$

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