# arrow_back Find the first 3 terms in ascending powers of $x$ of the binomial expansion of $\left(2+\frac{x}{2}\right)^{6}$

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(a) Find the first 3 terms in ascending powers of $x$ of the binomial expansion of $\left(2+\frac{x}{2}\right)^{6}$

(b) Use your expansion to find an estimate for the value of $2.05^{6}$

(a)

$1(2)^{6}+6(2)^{5}\left(\frac{x}{2}\right)+15(2)^{4}\left(\frac{x}{2}\right)^{2}$
$= 64+96 x+60 x^{2}$

(b)

\begin{aligned}\left(2+\frac{x}{2}\right)^{6} &=2.05^{6} \\ 2+\frac{x}{2} &=2.05 \\ \frac{x}{2} &=0.05 \\ x &=0.1 \\=74.2 & \\=& \\=& \\=& \\=& \\ 24.1 &+60(0.1)^{2} \end{aligned}
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