Multiple choice

The sum of n terms of the series 4 + 44 + 444 +.... is

  1. (4/81) [10n+1 - 9n - 1]

  2. (4/81) [10n-1 - 9n - 1]

  3. (4/81) [10n+1 - 9n - 10]

  4. (4/81) [10n - 9n - 10]
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C Correct answer
Explanation

The series 4 + 44 + 444 + ... can be rewritten as (4/9) * (9 + 99 + 999 + ...), which becomes (4/9) * [(10 - 1) + (10^2 - 1) + ... + (10^n - 1)]. Summing the geometric progression and the constant term yields the standard closed-form expression (4/81) * [10^(n+1) - 9n - 10].

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