What are some examples of convergent series?
Here are three significant examples...
#sum_(n=0)^oo (r^n a_0) = a_0/(1-r)#
The series defining
#e^x = sum_(n=0)^oo x^n/(n!)#
To prove this, for any given
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#