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**Find**the radius**of convergence**and the**interval of convergence**for the following infinite series, with n = 0 as the starting index: S = > You will be graded on the following: +2: Ratio Test (with algebraic details as shown in lecture materials) +1: Radius**of convergence**clearly stated and boxed +2: Formal testing of lower endpoint in**interval**(includes formal series test names and- The result will be an open
**interval**, a half-open**interval**or a closed**interval**. We call this**interval**, the**interval****of****convergence**. Notice the difference between the terms radius of**convergence**and**interval****of****convergence**. The radius of**convergence**gives information about the open**interval**but says nothing about the endpoints. - TikTok video from maha babar (@mahababar): "How does one
**find**the**interval**of**convergence**". T-10 hours. original sound. - Rate of
**Convergence**for the Bracket Methods •The rate of**convergence****of**-False position , p= 1, linear**convergence**-Netwon 's method , p= 2, quadratic**convergence**-Secant method , p= 1.618 . -Fixed point iteration , p= 1, linear**convergence**•The rate value of rate of**convergence**is just a theoretical index of**convergence**in general. - The sum of those terms can either be finite or infinite. The series converges if the sum of those terms is a finite number. The series diverges if the sum of those terms is infinite. By solving for the
**interval****of****convergence**, we**find**the range of values for x in |x - a| < R such that the series converges. Why do we Learn**Interval****of****Convergence**?