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TIFR-2019-Maths-A: 1

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The following sum of numbers (expressed in decimal notation)

$$1+11+111+\cdots +\underset{n}{\underbrace{11\dots1}}$$

is equal to

  1. $\left ( 10^{n+1}-10-9n \right )/81$
  2. $\left ( 10^{n+1}-10+9n \right )/81$
  3. $\left ( 10^{n+1}-10-n \right )/81$
  4. $\left ( 10^{n+1}-10+n \right )/81$
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