Question

$7+77+777+\dots \dots +(777\dots 7n$ times $)=$

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

Answer 1

The correct option is A $\frac{7}{81}({10}^{n+1}-9n-10)$

$t_r=7.(1+10+{10}^2+...+{10}^{r-1})=\frac{7({10}^r-1)}{9}$

$S=\frac{7}{9}\Sigma {10}^r-\frac{n}{9}$

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

$S=\frac{7({10}^{n+1}-9n-10)}{81}$