Question

The sum of the first 10 terms of the series 9 + 99 + 999 + ..., is ______.

Options

• `9/8(9^10 - 1)`

• `100/9(10^9 - 1)`

• 10⁹ – 1

• `100/9(10^10 - 1)`

Answer 1

The sum of the first 10 terms of the series 9 + 99 + 999 + ..., is `underlinebb(100/9(10^9 - 1))`.

Explanation:

9 + 99 + 999 + ........ upto 10 terms

= (10 – 1) + (100 – 1) + (1000 – 1) + ........ upto 10 terms

= (10 + 100 + 1000 + .......... upto 10 terms) – (1 + 1 + ... upto 10 times)

= `(10[10^10 - 1])/(10 - 1) - 10`

= `(10(10^10 - 1))/9 - 10`

= `(10^11 - 10 - 90)/9`

= `(10^11 - 100)/9`

= `(100(10^9 - 1))/9`