CA Foundation P3 · Chapter 6 · Question 9 of 9
The sum of the first n terms of the series 0.7 + 0.77 + 0.777 + ... is:
Test yourself: pick an answer
Reveal answer & explanation
Correct answer: D) (7/81)(9n − 1 + 10⁻ⁿ)
Explanation
Write S = (7/9)[0.9 + 0.99 + 0.999 + ...] = (7/9)[(1 − 0.1) + (1 − 0.01) + ...] = (7/9)[n − (0.1)(1 − 10⁻ⁿ)/0.9] = (7/9)[n − (1 − 10⁻ⁿ)/9] = (7/81)(9n − 1 + 10⁻ⁿ). Check n = 2: (7/81)(17.01) = 1.47 = 0.7 + 0.77.
More Sequence and Series - Arithmetic and Geometric Progressions MCQs
- Q2The sum of the first 20 terms of the A.P. 3, 8, 13, ... is:
- Q3How many terms of the A.P. 5, 9, 13, ... must be taken so that their sum is 230?
- Q4The 8th term of the G.P. 3, 6, 12, 24, ... is:
- Q5The sum to infinity of the G.P. 12, 4, 4/3, ... is:
- Q6The sum of the first 6 terms of the G.P. 2, 6, 18, ... is: