Chapter 12 Sequences and Series - 12.4 Find Sums of Infinite Geometric Series - 12.4 Exercises - Skill Practice - Page 823: 26

$\dfrac{16}{99}$

Here, we have $a_n= a_1 r^{n-1}$ for the Geometric series. Re-arrange the given series as: $0.161616...=0.16 +0.16 (0.01) +0.16(0.1)^2 +....$ First term $a_1=0.16$ and Common ratio $r=0.01$ The sum of an infinite Geometric Series can be found using: $S_n=\dfrac{a_1}{1-r}$ Thus, $S_n=\dfrac{0.16}{1-0.01}$ Hence, $S_n=\dfrac{16}{99}$