Find the sum of the following series: `9+99+999+ to\ n\ t e r m s`

Explanation

Given, `9+99+999+.... `upto n terms

we can write this series in this form

` s=(10−1)+(100−1)+(1000−1).......` up to n terms.

`=[(10+100+1000+......)+(−1−1−1−.......up to n terms)]`

=`[(10+10^2+10^3+.....up to n terms)−n] ` ........(i)

sum of n terms of GP. =`a(r^n−1)/(r-1)`

​, where a is first term and r is the common ratio of the GP.

We have the GP `10+10^2+10^3+....up to n `

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