Obtain the first $4$ terms in the expansion, in ascending powers of $x$, of \({{\left( 1+2x \rig

Question

Obtain the first $4$ terms in the expansion, in ascending powers of $x$, of ${{\left( 1+2x \right)}^{4}}$. Hence, find the value of ${{\left( 1.03 \right)}^{4}}$ correct to $3$ decimal places.

Accepted Answer

$1+8x+24x^2+32x^3+\cdots$; $(1.03)^4\approx1.126$ (3 d.p.).

Maclaurin Series and Power Series - Approximations Using Power Series

Maclaurin Series and Power Series - Approximations Using Power Series

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