Indian Institute of Foreign Trade 2016 Solved Paper

(c) Here, 4 + 44 + 444 + -------------- n terms
= 4 (1 + 11 + 111 + -------------- n terms)
$=\frac{4}{9}$(9 + 99 + 999 + -------------- n terms)
$=\frac{4}{9}$[(10 – 1) + (100 – 1) + (1000 – 1) +--------- + n terms]
$=\frac{4}{9}$[10 + 100 + 1000 + -------------- – n]
$=\frac{4}{9}\left[\frac{10\left({10}^{\mathit{n}}-1\right)}{9}-\mathit{n}\right]$
$=\frac{40}{81}\left({10}^{\mathit{n}}-1\right)-\frac{4\mathit{n}}{9}$