Let be the function .

MATHEMATICS · Multi-part · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Let

h

be the function

h(x)=\dfrac{2x^{2}}{1-4x}

. (a) Express

h(x)

as a power series in powers of

x

centered at

0

. Write the series in expanded form and provide the first four non-zero terms. (b) Determine the interval of

x

-values for which the series found in part (a) converges. Show your reasoning.