Chapter 12 Sequences and Series - 12.4 Find Sums of Infinite Geometric Series - 12.4 Exercises - Skill Practice - Page 823: 32

$C$

Here, we have $a_n= a_1 r^{n-1}$ for the Geometric series. Re-arrange the given series as: $18.1818181....=18.\overline{18}=18+\dfrac{18.\overline{18}}{100}$ $1.\overline{18} \times (1-\dfrac{1}{100})=18$ or, $1.\overline{18} \times \dfrac{99}{100}=18$ or, $1.\overline{18} = \dfrac{1800}{99}=\dfrac{200}{11}$ Hence, the correct option is $C$.