# How do you find the power series representation of a function?

In mathematics, the power series method is used to find the solution of the differential equation of certain differential equations. We can use the power series calculator to find the solution of the function. We find the solution of the value of the unknown coefficient and then put the value of the coefficient to find the solution of the equation.

## The application of the power series:

There is a wide range of applications of the power series in mathematics.

• The power series is used to expand and solve the other functions, and solve equations, in mathematics its utilization is wide, we can use the power series calculator to find the solution of the equations, sometimes students find it difficult to expand the function and to find its derivatives, you find the expansion of the power series by using power series expansion calculator.
• The power series is used in the convergence of an interval, and in the assessment of a trial function, the power function is widely applied in all areas of engineering.
• We also use Taylor’s series to find out the solution to the power series question. It makes the calculation a little easier for the students.
• Taylor’s series is also important in calculating the numerical approximation to different questions, especially when we have to solve the derivatives of multiple variables.

### How we can use the power series:

We can generate the power series representation by manipulating a standard power series as:

f(x)= ​1/1-X=1+X​+X2+X3….=n=0xn

The main goal of the power series is to utilize the differentiation to the left side of the equation. We have to do the differentiate all the three parts of the left side of the equation. The values can be differentiated into the infinite values of the power of the x, but we stop at the first power of the values of the x and then use the dots to show the value is increasing to the infinite solution.

We simplify the sum by using the summation characters, that the sum is starting from the value of the X from 1 to infinity, the result will be a power series representation of a function. We can also find the radius of the interval by using the power series representation of the convergence of the function. The power series solution calculator can be used in finding the solution of the power function.

### Why do power series converge and diverge:

Since we use a certain limit or values of the function x, the values of the function f(x) converge between the limit and diverge outside a certain limit of the function f(x). For example, there is a limit of (-2,2) of function f(x). When we take the derivative of the values and apply the limit, the values of the function f(x), Converge between the limit (-2,2), and it diverges outside the limit for the infinite values of the function f(x). You can use the Power Series Calculator to represent a function of a power series up to the “n” values.

If we want to represent a power function of a limit  (-2,2) and a power of “n” of the X, we can represent the values as:

n=-22xn

So values between (-2,2) of the values of the function would converge between the limit and the remaining values diverge outside the limit for the infinite values of the function f(x). The main reason for this is that the values are outside the given limit of the function. The Power Series Calculator is an easy method of finding all the derivatives of the function within the given limit.

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