How can I tell whether a geometric series converges?
1 Answer
A geometric series of geometric sequence
Explanation:
The standard form of a geometric sequence is :
And a geometric series can be written in several forms :
Let
Let's calculate
Therefore, the geometric series can be written as :
Thus, the geometric series converges only if the series

If r > 1 :
#lim_(n>+oo)((1  r^n)/(1r)) = oo# 
If r < 1 :
#lim_(n>+oo)((1  r^n)/(1r)) = 1/(1r)# .
Therefore, the geometric series of geometric sequence