# What are some examples of convergent series?

##### 1 Answer

Nov 1, 2015

Here are three significant examples...

#### Explanation:

**Geometric series**

If

#sum_(n=0)^oo (r^n a_0) = a_0/(1-r)#

**Exponential function**

The series defining

#e^x = sum_(n=0)^oo x^n/(n!)#

To prove this, for any given

**Basel problem**

The Basel problem, posed in 1644 and solved by Euler in 1734 asked for the value of the sum of reciprocals of squares of positive integers:

#sum_(n=1)^oo 1/(n^2) = pi^2/6#