Answer
$c_0$
$c_0+c_1x$
$c_0+c_1x+c_2x^2$
$c_0+c_1x+c_2x^2+c_3x^3$
Work Step by Step
The general form of a power series is:
$\sum_{k=0}^{\infty} c_k(x-a)^k$
As the series is centered to 0, rewrite the expression for $a=0$:
$\sum_{k=0}^{\infty} c_k x^k$
Determine the first 4 terms:
$\sum_{k=0}^{0}c_k\cdot x^k=c_0x^0=c_0$
$\sum_{k=0}^{1}c_k x^k=c_0+c_1x$
$\sum_{k=0}^{2}c_k x^k=c_0+c_1x+c_2x^2$
$\sum_{k=0}^{3}c_k x^k=c_0+c_1x+c_2x^2+c_3x^3$
