Final answer:
True. A power series can generate the series representation of a given function.
Step-by-step explanation:
True. A power series can generate the series representation of a given function.
A power series is an infinite sum of terms, where each term involves powers of a variable. The coefficients and powers in the series can be chosen in such a way that the series converges to a specific function when the variable is within a certain range.
For example, the power series for the exponential function can be written as:
- e^x = 1 + x + (x^2/2!) + (x^3/3!) + ...
This power series can generate the exponential function, which is given by the equation e^x in calculus.