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The sum upto infinity of the series 4/7-5/7^(2) 4/7^(3)-5/7^(4) . is (a) 23/48 (b) 25/48 (c) 1/2 (d) None of these?
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The sum upto infinity of the series 4/7-5/7^(2) 4/7^(3)-5/7^(4) . is (...
Solution:
The given series is 4/7-5/7^(2) + 4/7^(3)-5/7^(4) + ...
We can write this series as (4/7-5/7^(2)) + (4/7^(3)-5/7^(4)) + ...
Let's consider the first term of the series separately.
First Term:
4/7-5/7^(2) = (4*7-5)/7^(2) = 23/7^(2)
Second Term:
4/7^(3)-5/7^(4) = (4*7-5)/7^(4) = 23/7^(4)
Third Term:
4/7^(5)-5/7^(6) = (4*7-5)/7^(6) = 23/7^(6)
General Term:
The general term of the series is given by (4/7^(2n-1)) - (5/7^(2n))
= (4*7^(2n) - 5*7^(2n-1))/7^(2n)
= 7^(2n-1)/7^(2n) * (4*7 - 5)
= 23/7^(2n)
Sum of the Series:
The sum of the series can be given by the formula:
Sum = a/(1-r)
where a is the first term of the series and r is the common ratio.
Here, a = 23/7^(2) and r = 1/7^(2).
Substituting the values in the formula, we get:
Sum = (23/7^(2))/(1-1/7^(2))
= (23/7^(2))/(48/7^(2))
= 23/48
Therefore, the sum of the series is 23/48.
Hence, option (a) 23/48 is the correct answer.
The given series is 4/7-5/7^(2) + 4/7^(3)-5/7^(4) + ...
We can write this series as (4/7-5/7^(2)) + (4/7^(3)-5/7^(4)) + ...
Let's consider the first term of the series separately.
First Term:
4/7-5/7^(2) = (4*7-5)/7^(2) = 23/7^(2)
Second Term:
4/7^(3)-5/7^(4) = (4*7-5)/7^(4) = 23/7^(4)
Third Term:
4/7^(5)-5/7^(6) = (4*7-5)/7^(6) = 23/7^(6)
General Term:
The general term of the series is given by (4/7^(2n-1)) - (5/7^(2n))
= (4*7^(2n) - 5*7^(2n-1))/7^(2n)
= 7^(2n-1)/7^(2n) * (4*7 - 5)
= 23/7^(2n)
Sum of the Series:
The sum of the series can be given by the formula:
Sum = a/(1-r)
where a is the first term of the series and r is the common ratio.
Here, a = 23/7^(2) and r = 1/7^(2).
Substituting the values in the formula, we get:
Sum = (23/7^(2))/(1-1/7^(2))
= (23/7^(2))/(48/7^(2))
= 23/48
Therefore, the sum of the series is 23/48.
Hence, option (a) 23/48 is the correct answer.
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The sum upto infinity of the series 4/7-5/7^(2) 4/7^(3)-5/7^(4) . is (a) 23/48 (b) 25/48 (c) 1/2 (d) None of these?
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The sum upto infinity of the series 4/7-5/7^(2) 4/7^(3)-5/7^(4) . is (a) 23/48 (b) 25/48 (c) 1/2 (d) None of these? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The sum upto infinity of the series 4/7-5/7^(2) 4/7^(3)-5/7^(4) . is (a) 23/48 (b) 25/48 (c) 1/2 (d) None of these? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum upto infinity of the series 4/7-5/7^(2) 4/7^(3)-5/7^(4) . is (a) 23/48 (b) 25/48 (c) 1/2 (d) None of these?.
The sum upto infinity of the series 4/7-5/7^(2) 4/7^(3)-5/7^(4) . is (a) 23/48 (b) 25/48 (c) 1/2 (d) None of these? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The sum upto infinity of the series 4/7-5/7^(2) 4/7^(3)-5/7^(4) . is (a) 23/48 (b) 25/48 (c) 1/2 (d) None of these? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum upto infinity of the series 4/7-5/7^(2) 4/7^(3)-5/7^(4) . is (a) 23/48 (b) 25/48 (c) 1/2 (d) None of these?.
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