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the sum of the series 4 + 44 + 444 + .... upto n term isIf 1 + 10 + 10² + ......... upto n terms = 10&supn; - 1 , then 9
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4 (10n - 1) - 4n 9 9 -
4 (10n - 1)- 4n 81 9 -
40 (10n - 1)- 4n 81 9 -
40 (10n - 1)- 4n 9 9
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Correct Option: C
Expression = 4 + 44 + 444 + ..... to n terms = 4 (1 + 11 + 111 + .....to n terms)
On multiplying by 9 and divided by 9 , we get
| Expression = | (9 + 99 + 999 + ..... to n terms) | |
| 9 |
| = | [(10 - 1) + (100 - 1) + (1000 - 1) + ..... to n terms] | |
| 9 |
| = | [(10 + 10² + 10³ + ..... to n terms) - n][ ∵ 1 has been added n times ] | |
| 9 |
| = | [10(1 + 10 + 10² + ..... to n terms) - n] | |
| 9 |
| = | . | - | n | |||
| 9 | 9 | 9 |
 | ∵ 1 + 10 + 102 + ..... to n terms = |  | |
| 9 |
| Expression = | (10n - 1) - | n | ||
| 81 | 9 |
