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The sum of n terms of the series 7+77+777+……is a)(7/9)[(1/9)(10n+1-10)-n] b) (9/10)[(1/9)(10n+1-10)-n] c)(10/9)[(1/9)(10n+1-10)-n] d)None Correct answer is option 'A'. Can you explain this answer?
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The sum of n terms of the series 7+77+777+……is a)(7/9)[(1/9)(10n+1-10)...
Solution:
The given series is 7, 77, 777, 7777, …
We can observe that the nth term of the series is given by (7 × (10n – 1))/9.
Let Sn be the sum of n terms of the series.
Then,
Sn = 7 + 77 + 777 + ….. to n terms
Sn = (7 × 1) + (7 × 11) + (7 × 111) + ….. to n terms
Sn = 7(1 + 11 + 111 + ….. to n terms)
Sn = 7 × (111…n times – 1)/10 – 1) (as 1 + 11 + 111 + ….. to n terms is a GP with a = 1, r = 10, and n terms)
Sn = (7/9) × (10n – 1) – 7/9 (sum of GP formula)
Sn = (7/9) × (10n – 1 – 9) (taking 9 common)
Sn = (7/9) × (10n – 10)
Sn = (7/9) × 10 × [(1/9) (10n – 1) – 1] (taking 10 common and simplifying)
Sn = (7/9) × 10 × [(1/9) (10n – 1) – n/10] (using the formula for sum of n terms of GP)
Sn = (7/9) × [(1/9) (10n – 1) – n] (simplifying)
Hence, option A is the correct answer.
The given series is 7, 77, 777, 7777, …
We can observe that the nth term of the series is given by (7 × (10n – 1))/9.
Let Sn be the sum of n terms of the series.
Then,
Sn = 7 + 77 + 777 + ….. to n terms
Sn = (7 × 1) + (7 × 11) + (7 × 111) + ….. to n terms
Sn = 7(1 + 11 + 111 + ….. to n terms)
Sn = 7 × (111…n times – 1)/10 – 1) (as 1 + 11 + 111 + ….. to n terms is a GP with a = 1, r = 10, and n terms)
Sn = (7/9) × (10n – 1) – 7/9 (sum of GP formula)
Sn = (7/9) × (10n – 1 – 9) (taking 9 common)
Sn = (7/9) × (10n – 10)
Sn = (7/9) × 10 × [(1/9) (10n – 1) – 1] (taking 10 common and simplifying)
Sn = (7/9) × 10 × [(1/9) (10n – 1) – n/10] (using the formula for sum of n terms of GP)
Sn = (7/9) × [(1/9) (10n – 1) – n] (simplifying)
Hence, option A is the correct answer.
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The sum of n terms of the series 7+77+777+……is a)(7/9)[(1/9)(10n+1-10)-n] b) (9/10)[(1/9)(10n+1-10)-n] c)(10/9)[(1/9)(10n+1-10)-n] d)None Correct answer is option 'A'. Can you explain this answer?
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The sum of n terms of the series 7+77+777+……is a)(7/9)[(1/9)(10n+1-10)-n] b) (9/10)[(1/9)(10n+1-10)-n] c)(10/9)[(1/9)(10n+1-10)-n] d)None Correct answer is option 'A'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The sum of n terms of the series 7+77+777+……is a)(7/9)[(1/9)(10n+1-10)-n] b) (9/10)[(1/9)(10n+1-10)-n] c)(10/9)[(1/9)(10n+1-10)-n] d)None Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of n terms of the series 7+77+777+……is a)(7/9)[(1/9)(10n+1-10)-n] b) (9/10)[(1/9)(10n+1-10)-n] c)(10/9)[(1/9)(10n+1-10)-n] d)None Correct answer is option 'A'. Can you explain this answer?.
The sum of n terms of the series 7+77+777+……is a)(7/9)[(1/9)(10n+1-10)-n] b) (9/10)[(1/9)(10n+1-10)-n] c)(10/9)[(1/9)(10n+1-10)-n] d)None Correct answer is option 'A'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The sum of n terms of the series 7+77+777+……is a)(7/9)[(1/9)(10n+1-10)-n] b) (9/10)[(1/9)(10n+1-10)-n] c)(10/9)[(1/9)(10n+1-10)-n] d)None Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of n terms of the series 7+77+777+……is a)(7/9)[(1/9)(10n+1-10)-n] b) (9/10)[(1/9)(10n+1-10)-n] c)(10/9)[(1/9)(10n+1-10)-n] d)None Correct answer is option 'A'. Can you explain this answer?.
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