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The sum upto infinity of the series 1/2+1/6+1/18+……is
- a)3/4
- b)1/4
- c)1/2
- d)None
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The sum upto infinity of the series 1/2+1/6+1/18+……isa)3...
To find the sum up to infinity of the series 1/2, 1/6, 1/18..., we can use the formula for the sum of an infinite geometric series, which is:
S = a / (1 - r)
where S is the sum, a is the first term, and r is the common ratio.
In this series, the first term a = 1/2, and the common ratio r = 1/3, since each term is one-third of the previous term.
Plugging these values into the formula, we get:
S = (1/2) / (1 - 1/3)
S = (1/2) / (2/3)
S = 3/4
Therefore, the sum up to infinity of the series 1/2, 1/6, 1/18... is 3/4.
S = a / (1 - r)
where S is the sum, a is the first term, and r is the common ratio.
In this series, the first term a = 1/2, and the common ratio r = 1/3, since each term is one-third of the previous term.
Plugging these values into the formula, we get:
S = (1/2) / (1 - 1/3)
S = (1/2) / (2/3)
S = 3/4
Therefore, the sum up to infinity of the series 1/2, 1/6, 1/18... is 3/4.
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The sum upto infinity of the series 1/2+1/6+1/18+……isa)3/4b)1/4c)1/2d)NoneCorrect answer is option 'A'. Can you explain this answer?
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