The Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivates at a single point. Its utility could be to graphically represent functions by selecting a sufficient number of terms and thus decreasing the error gradually.

or, in expanded form:

For the case , the series is a particular case of the Taylor Series, called the Maclaurin series.

Find the Maclaurin expansion for :

which is a repeating pattern.

Now we expand the coefficients:

observing that certain nominators contain and can be reduced, we obtain the final formula for :

Using the alternating series procedure, the series converges because:

and

fuss/mathematics/calculus/series.txt ยท Last modified: 2017/02/22 18:30 (external edit)

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