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The sum upto infinity of the series 2/3+5/9+2/27+5/81+…..is
- a)11/8
- b)8/11
- c)3/11
- d)None
Correct answer is option 'A'. Can you explain this answer?
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The sum upto infinity of the series 2/3+5/9+2/27+5/81+…..isa)11...
To find the sum upto infinity of the series, we need to first determine its common ratio.
The first term is 2/3 and the second term is 5/9. To get from the first term to the second term, we multiply by 5/3. Similarly, to get from the second term to the third term, we multiply by 2/3.
Therefore, the common ratio is (2/3)*(5/3) = 10/9.
Now we can use the formula for the sum of an infinite geometric series:
S = a/(1-r)
where S is the sum, a is the first term, and r is the common ratio.
Plugging in the values from our series, we get:
S = (2/3)/(1-10/9) = (2/3)/(-1/9) = -6
Therefore, the sum of the series upto infinity is -6.
The first term is 2/3 and the second term is 5/9. To get from the first term to the second term, we multiply by 5/3. Similarly, to get from the second term to the third term, we multiply by 2/3.
Therefore, the common ratio is (2/3)*(5/3) = 10/9.
Now we can use the formula for the sum of an infinite geometric series:
S = a/(1-r)
where S is the sum, a is the first term, and r is the common ratio.
Plugging in the values from our series, we get:
S = (2/3)/(1-10/9) = (2/3)/(-1/9) = -6
Therefore, the sum of the series upto infinity is -6.
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