91Ó°ÊÓ

Find the Taylor or Maclaurin series of the given function with the given point as center and determine the radius of convergence. $$\cos ^{2} z, \quad 0$$

Find the center and the radius of convergence of the following power series. (Show the details.) $$\sum_{n=0}^{\infty} \frac{n !}{n^{n}}(z+1)^{n}$$

Are the following sequences \(z_{1}, z_{2}, \cdots, z_{n}, \cdots,\) bounded? Convergent? Find their limit points, (Show the details of your work.) $$z_{n}=(3+4 i)^{n} / n !$$

Find the center and the radius of convergence of the following power series. (Show the details.) $$\sum_{n=0}^{\infty} \frac{2^{100 n}}{n !} z^{n}$$

Find the Taylor or Maclaurin series of the given function with the given point as center and determine the radius of convergence. $$1 / Z, \quad 1$$

Find the center and the radius of convergence of the following power series. (Show the details.) $$\sum_{n=0}^{\infty}\left(\frac{a}{b}\right)^{n} z^{n}$$

Are the following sequences \(z_{1}, z_{2}, \cdots, z_{n}, \cdots,\) bounded? Convergent? Find their limit points, (Show the details of your work.) $$z_{m}=\sin (n \pi / 4)+i^{n}$$

Find the Taylor or Maclaurin series of the given function with the given point as center and determine the radius of convergence. $$1 /(1-z), \quad 1$$

Are the following sequences \(z_{1}, z_{2}, \cdots, z_{n}, \cdots,\) bounded? Convergent? Find their limit points, (Show the details of your work.) $$z_{n}=\left[(1+30 \sqrt{10}]^{n}\right.$$

Find the center and the radius of convergence of the following power series. (Show the details.) $$\sum_{n=0}^{\infty}(n-i)^{n} z^{n}$$