![Q.7 The sum of n terms of the series 4 + 44 + 444 + … is Options: (A) (4/81) [10n+1 − 9n − 1] (B) (4/81) [10n − 9n − 1] (C) (4/81) [10n+1 − 9n − 10] (D) (4/81) [10n − 9n − 10]](https://www.letstalkacademy.com/wp-content/uploads/2026/01/slide_7-16.png)
Q.7
The sum of n terms of the series 4 + 44 + 444 + … is
Options:
(A) (4/81) [10n+1 − 9n − 1]
(B) (4/81) [10n − 9n − 1]
(C) (4/81) [10n+1 − 9n − 10]
(D) (4/81) [10n − 9n − 10]
Sum of n Terms of the Series 4 + 44 + 444 + …
The series 4 + 44 + 444 + … is a commonly asked question in competitive exams.
In this solution, we derive the general formula for the sum of n terms and
identify the correct option.
Step-by-Step Solution
Step 1: General Term
The nth term of the series is:
an = 4 × (10n − 1) / 9
Step 2: Sum of n Terms
Sn = (4/9) Σ (10k − 1), where k = 1 to n
Step 3: Evaluate the Summation
Σ10k = 10(10n − 1)/9
Σ1 = n
Step 4: Simplification
Sn = (4/9) [10(10n − 1)/9 − n]
Sn = (4/81) [10n+1 − 9n − 10]
Correct Answer
Option (C)
Sn = (4/81) [10n+1 − 9n − 10]
Conclusion
The correct formula for the sum of n terms of the series
4 + 44 + 444 + … is:
Sn = (4/81) [10n+1 − 9n − 10]
