express-mzz51z-mz-fracz51-z-as-a-power-series-centered-at-00-what-is-its-interva

Question

Express m(z)=z51−z m(z) = \frac{$$z^5$$}{1-z}  as a power series centered at 00. What is its interval of convergence?

Accepted Answer

∑k=5∞zk\displaystyle\sum_{k=5}^{\infty} z^k(−1,1)\left(-1,1\right)

Answer

∑k=0∞zk{\displaystyle\sum_{k=0}^{\infty}$$z^{k}$$}(−1,1)\left(-1,1\right)

Answer

∑k=5∞zk\displaystyle\sum_{k=5}^{\infty} z^k[−1,1]\left\lbrack-1,1\right\rbrack

Answer

∑k=2∞zk{\displaystyle\sum_{k=2}^{\infty}$$z^{k}$$}(−1,1)\left(-1,1\right)

Express m(z)=z51−z m(z) = \(\frac{z^5}{1-z}\) as a power series centered at 00. What is its interval of convergence?