Define (g(x)= _ n=0 ^ (-1)^ n x^ 2n+1 2n+1 ) for (|x|<1 )

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Define

g(x)=\displaystyle\sum_{n=0}^{\infty}(-1)^{n}\frac{x^{2n+1}}{2n+1}

for

|x|<1

. Using the first three nonzero terms of the series, compute a numerical approximation of

g(0.3)

accurate to four decimal places.