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.

The entrances to these programs are far more challenging than usual engineering entrances. Cheenta offers an intense, problem-driven program for these two entrances.

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