The power series is .

(a)

Graph several partial terms of the series.

.

Graph :

Graph the partial sums.

(b)

Find the sum of the series and its radius of convergence.

The power series is .

Rewrite the series.

Since .

The series is converges if .

The series is converges in the interval and the radius of convergence is .

(c)

Find the approximate sum when .

The power series is .

Substitute .

.

(d)

Find the good approximation.

.

(a)

Graph :

Graph of the partial sums.

(b) The series is converges in the interval and the radius of convergence is .

(c)

(d) The error is .