Understand the problem

 Find the sum 1+111+11111+1111111+…..1….111(2k+1) ones 

 

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

 

 

 

Connected Program at Cheenta

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

Indian Statistical Institute and Chennai Mathematical Institute offer challenging bachelor’s program for gifted students. These courses are B.Stat and B.Math program in I.S.I., B.Sc. Math in C.M.I.

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