Exam 11: Taylor Polynomials and Infinite Series

Find the general term of the sequence. ​

Determine whether the following series is convergent or divergent. ​

Consider the series ​ . ​ Find the values of x for which the series converges. ​ Find the sum of the series where it is convergent.

Determine whether the following series is convergent or divergent. ​

Find the Taylor series of the function at the indicated point. Give the interval of convergence for the series. ​

Consider the series . ​ Find the radius of convergence of the power series. ​ __________ ​ Find the interval of convergence of the power series. ​ __________

Consider the series . ​ Find the radius of convergence of the power series. ​ __________ ​ Find the interval of convergence of the power series. ​ __________

Consider the series ​ . ​ Determine whether the geometric series converges or diverges. ​ If it converges, find its sum.

Use the eighth-degree Taylor polynomial to approximate ​ ​ Round the answer to four decimal places, if necessary.

Use the Newton method to approximate the indicated zero of the function. Continue with the iteration until two successive approximations differ by less than 0.0001. Round your answer to four decimal places, if necessary. ​ The zero of between and , .