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 limn→∞ rn = 0. Thus despite the infinite number of tribes, the sum of all the term tribes is not limited.
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.
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:
So length of the ball paths is 30m.
Similarly this article.
Sorry if there is a wrong word.
The end of word wassalamualaikum wr. wb
Referensi :
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 limn→∞ 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:
So length of the ball paths is 30m.
Similarly this article.
Sorry if there is a wrong word.
The end of word wassalamualaikum wr. wb
Referensi :
- To'Ali's book math group accounting and sales
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