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#