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Series

Find 9 S n - ...

Question

Find $9 (S_{n} - S_{n - 1})$ if $S_{n} (1 \leq n \leq 9)$ is the sum to n terms of the following series 1+22+333+4444+...999999999

10ⁿ –n² +n

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n(10ⁿ-1)

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n(100ⁿ-2)

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n²+10n

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Solution

The correct option is B n(10ⁿ-1)
Put n=2,
$S_{2} - S_{1} = 23 - 1 = 22$
$9 (S_{2} - S_{1}) = 198$
On substituting n=2, only option B gives 198.

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