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Question : 2 of 120
Marks:
+1,
-0
Solution:
Concept:
Geometric Progression (GP):
- The series of numbers where the ratio of any two consecutive terms is the same is called a Geometric Progression.
- A Geometric Progression of n terms with first term a and common ratio r is represented as: a, ar, ar 2,ar3,...,arn−2,arn−1.
- The sum of the first n terms of a GP is: Sn=a(‌).
- The sum to ∞ of a GP, when |r|<1, is: S∞=‌.
Calculation:
Let us consider the infinite series
‌+‌+‌+...∞.
Here,
a=‌ and
r=‌=‌.
∴S∞=‌=‌=‌=‌ Now, let
P=9‌9‌9‌...∞ ∴P=9‌+‌+‌+...∞=9‌=√9=3.
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