Question

$7+77+777+....n$ terms $=$

• A. $\frac{70({10}^n-1)}{81}-\frac{7n}{9}$
• B. $\frac{7({10}^n-1)}{81}-\frac{7n}{9}$
• C. $\frac{60({10}^n-1)}{27}-\frac{2n}{3}$
• D. $\frac{60({10}^n+1)}{27}+\frac{2n}{3}$

Answer 1

Answer: (A)

$\frac{70({10}^n-1)}{81}-\frac{7n}{9}$

$7(1+11+111+....n$ terms)

$=\frac{7}{9}(9+99+999+...)$

$=\frac{7}{9}\times \left[\right(10-1)+(100-1)+(1000-1)....nterms]$
$=\frac{7}{9}\times [10+100+\mathrm{1000...}nterms-1-1-\mathrm{1...}nterms]$
$=\frac{7}{9}\times [\frac{10({10}^n-1)}{9}-n]$
$=\frac{70\times ({10}^n-1)}{81}-\frac{7n}{9}$
So the correct answer is A