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**Infinite Series Calculator: **Finding the sum of an infinite series of a function is not so simple or easy for any one. It will have difficult mathematical operations and it consumes your time and energy. So, we are coming up with the best solution for your problem by giving the free handy Infinite Series Calculator tool. You can also get the lengthy manual solution to solve the sum of the infinite series of a function. Make use of this free calculator tool to get accurate solutions for your function quickly.

Learn about how to solve the sum of infinite series of a function using this simple formula. Follow the below provided step by step procedure to obtain your answer easily.

- Take any function with the range to infinity to solve the infinite series
- Convert that function into the standard form of the infinite series
- Apply the infinite series formula
- Do all the required mathematical calculations to get the result

**Standard Form of Infinite Series**

Infinite series is defined as the sum of values in an infinite sequence of numbers. The notation Sigma (Σ) is used to represent the infinite series. The standard form of infinite series is

Σ_{0} ^{∞} r^{n}

Where 0 is the lower limit

∞ is the upper limit

r is the function

The formula to find the infinite series of a function is defined by

Σ_{0}^{∞} r^{n} = 1/(1-r)

**Example:**

**Question: solve the sum of Σ _{0}^{∞} 1/10^{n}?**

Solution:

Given function is 1/10^{n}

r=1/10

Infinite series formula is

Σ_{0}^{∞} r^{n} = 1/(1-r)

Σ_{0}^{∞ 1/10n=1/(1-1/10)}

=10/9

Σ_{0}^{∞ 1/10n=10/9}

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**1. Can an infinite series be calculated?**

We can calculate the sum of an infinite geometric series. The formula to solve the sum of infinite series is related to the formula for the sum of first n terms of a geometric series. Finally, the formula is Sn=a1(1-r^{n)/1-r.}

**2. What is the general formula for the sum of infinite geometric series?**

The formula to find the sum of an infinite geometric series is S=a1/1-r.

**3. What is r in a sequence?**

r is called common ratio. The number multiplied or divided at each stage of a geometric seque is the common ratio.

**4. What are the 4 types of sequences?**

Some of the sequences are Arithmetic Sequences, Geometric Sequences, Harmonic Sequences, and Fibonacci Numbers.

**5. What is meant by sequence and series?**

Sequence is a list of numbers that have been ordered sequentially. Series is defined as the sum of the sequence terms.