Last Activity: 9 Years ago
Hello student,
First of all a geometric progression or a geometric series is a series of terms in which the ratio of any two adjacent terms is constant.
Eg. 2,,4 8, ….. is a geometric progression where the common ratio i.e. r = 2.
Now we discuss how to find the sum of infinite Geometric Progression:
Firstly, the sum of n terms of a G.P. is given by
S = a1-rn/1-r, where r ≠ 1.
Now, if |r| < 1 and n → ∞ then rn → 0 and in this case geometric series will be summable upto infinity and its sum is given by S∞= a/1-r.
I’ll consider one example here based on this concept:
Eg: The sum of an infinite number of terms of a G.P. is 15 and the sum of their squaresis 45. Find the series.
Sol: We have a + ar + ar2 + ar3 + ....... = 15
so, a/1-r = 15.
a2 + ar2 + ar22 +.... = 45
1-r/1+r = 1/5
Solving this we get 5-5r = 1+r.
So r = 2/3.
so, a = 151-r = 151-2/3 = 5.
so the series is 5, 10/3, 20/9, ….. .
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