a. Differentiate the Taylor series centered at 0 for the following functions.
b. Identify the function represented by the differentiated series.
c. Give the interval of convergence of the power series for the derivative.
Taylor series of function f(x) at a is defined as:
Consider the given:
b) The series sum representation-
Apply ratio test and find interval of convergence.
Consider the given series:
From ratio test, if L > 1 series diverges.
L< 1 series converges.
||x||<1 series converges.
Find the interval of convergence.
Interval of convergence
Interval of convergence =(-1,1]
Missing number in the series
Write the following arithmetic series in summation notation.