CA Foundation Exam > CA Foundation Questions > The sum upto infinity of the series 4/7-5/7^(...
Start Learning for Free
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?
Most Upvoted Answer
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.
Attention CA Foundation Students!
To make sure you are not studying endlessly, EduRev has designed CA Foundation study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CA Foundation.
|
Explore Courses for CA Foundation exam
|
|
Similar CA Foundation Doubts
Top Courses for CA FoundationView all
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?
Question Description
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?.
Solutions 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? in English & in Hindi are available as part of our courses for CA Foundation.
Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice CA Foundation tests.
|
|
Explore Courses for CA Foundation exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup