Infinite Geometry Series

The infinite geometry series is a convergent geometry series with infinite numbers. Because it has a ratio value between -1 to 1, the geometric series is not up to a geometric sequence down.

Since the r ratio is worth between -1 to 1, the next term will be smaller and will be close to zero, in other words lim_n→∞ rⁿ = 0. Thus despite the infinite number of tribes, the sum of all the term tribes is not limited.

Formula of Infinite Geometry Series

Information:
S_∞ = Unlimited geometry series
a = The first tribe
r = Ratio

Note:
It has a sum value of an infinite geometry series to only a series of convergent geometries, whereas the devergen geometry series of unlimited quantities do not exist.

Exmaple Question of Infinite Geometry Series

A reflected ball is dropped from a height of 6 meters. Each time a high fall of the ball reflection is reduced by one third of the previous high. Please determine the total number of ball paths until the ball stops.

Answer:

U₁ = 6
U₂ = 6 . 2/3 = 4
U₃ = 4 . 2/3 = 8/3
dan seterusnya..

The length of the ball path is 2 series of converging geometry, namely:
6 + 4 + 8/3 + .... and 4 + 8/3 + ...

the total number of ball paths: