Summary
Power series at a
Radius and interval of convergence
- possible intervals on which the series is convergent
Derivative and integral of power series
Concept
Power series
- resembles polynomials
congerges or diverges based on x
Power series representation of a function
proof in add link to cs1231s combinations and perms
Taylor and maclaurin series
- approximation of any function about a point
- based on higher order derivatives at that point
Application
Convergence of power series
power series default to using ratio test or root test
Interval on which the series is convergent
Power series representation and recognising the formula for convergent geometric series
Power series using integral
Maclaurin series of cosine
Maclaurin series representation of important functions