Mathematical Series

A mathematical series is the sum of the terms of a sequence of numbers. It is often represented using the summation notation ($\sum$).

• Geometric Series
• Taylor Series
• Harmonic Series

Other Examples

Sum of Positive Integers

The sum of the first $n$ positive integers is given by the formula:

$$\sum _{k=1}^{n}k=\frac{n(n+1)}{2}$$

where $S_n$ is the sum of the first $n$ integers.

Sum of Squares of Integers

The sum of the squares of the first $n$ positive integers is given by the formula:

$$\sum {k=1}^n{k}^2=\frac{n(n+1)(2n+1)}{6}$$

Sum of Cubes of Integers

The sum of the cubes of the first $n$ positive integers is given by the formula:

$$\sum _{k=1}^n{k}^3={\left(\frac{n(n+1)}{2}\right)}^2$$

Which is interestingly the square of the sum of the first $n$ integers.