Question

The sum of the series $12+104+1008+10016+...$ upto $n$ terms is

• A. $\frac{({10}^n-1)}{9}+2^n$
• B. $\frac{10({10}^n-1)}{9}+2(2^n-1)$
• C. $\frac{{10}^n-1}{9}-1$
• D. $\frac{10({10}^n-1)}{9}$

Answer 1

The correct option is B $\frac{10({10}^n-1)}{9}+2(2^n-1)$

Let, $S=12+104+1008+10016+...$ up to $n$ terms.

$S=(10+2)+(100+4)+(1000+8)+(10000+16)+....$ up to $n$ terms.

$S=(10+{10}^2+{10}^3+....+{10}^n)+2(1+2^1+2^2+....+2^{n-1})$
$S=\frac{10({10}^n-1)}{10-1}+\frac{2(2^n-1)}{2-1}$
$S=\frac{10({10}^n-1)}{9}+2(2^n-1)$