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