Question

Calculate the sum of the given series $1+11+111+1111+11111+.....$ upto $9$ terms:

• A. $123456789$
• B. $987654321$
• C. $999999999$
• D. None of these

Answer 1

The correct option is A $123456789$

$S=1+11+111+1111+...$ 9 terms

$\Rightarrow 9S=9+99+999+9999+...$ 9 terms

$\Rightarrow 9S=(10-1)+(100-1)+(1000-1)+(10000-1)+...$ 9 terms

$\Rightarrow 9S=[10+100+1000+10000+...$ 9 terms $]-9$

$\Rightarrow 9S=\left[\frac{10.({10}^9-1)}{10-1}\right]-9$

$\Rightarrow 9S=\left[1111111110\right]-9$

$\Rightarrow 9S=1111111101$

$\therefore S=123456789$