Binomial series

 Objective: write the terms of the binomial series

In previous post I showed how to find the Taylor series for some common function by calculating the coefficients of the Taylor polynomials. In posts relating to binomial series I will show how to use the Taylor series to derive the Taylor series of other functions. Later I will show how to use the Taylor series to solve integrals and differential equations.

 

Example

Solution

The function and the Mclaurin polynomial are graphed below:

The third Mclaurin polynomial provides a good approximation for f(x) = ⎷1 + x for x near 0.

Practice