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

1. (4/81) [10^(n+1) - 9n - 1]
2. (4/81) [10^(n-1) - 9n - 1]
3. (4/81) [10^(n+1) - 9n - 10]
4. (4/81) [10ⁿ - 9n - 10]

Correct answer: (4/81) [10^(n+1) - 9n - 10]

Solution

The sum is (4/9)[ (10^{n+1}-10)/9 - n ] = (4/81)[10^{n+1} - 9n - 10]. Checked at n=2 this gives 48, matching 4+44. The stored option uses -1 instead of -10 and is wrong; the correct one is option C.

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