## Understand the problem

##### Source of the problem

##### Topic

Algebra

##### Difficulty Level

3.5 out of 10

##### Suggested Book

challenges and trills of pre college mathematics

## Start with hints

Do you really need a hint? Try it first!

can you some how manipulate it in geometric progression .

\(\frac{1}{9}(9+99+999+9999………)\)

now can u transfer it into G.P series

ok let’s see

\(\frac{1}{9}[(10^1-1)+(10^2-1)+………] \) upto 2k+1 terms

= \(\frac{1}{9}[(10+10^2+10^3+……)-(1+1+1+1…….)]\)

now can u see the G.P Series , with first term 10 and common ratio 10

use the formula ,\( \frac{a(1-r^n)}{r-1}\)

so the final ans is \(\frac{1}{9}[\frac{10}{9}(10^{2k+1}-1)-n]\)

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# I.S.I. & C.M.I. Entrance Program

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