Chapter 12 Sequences and Series - 12.4 Find Sums of Infinite Geometric Series - 12.4 Exercises - Skill Practice - Page 823: 28

$\dfrac{3200}{99}$

Here, we have $a_n= a_1 r^{n-1}$ for the Geometric series. Re-arrange the given series as: $32.32323232...=32 +32 (0.01) +32(0.01)^2 +....$ First term $a_1=0.625$ 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, $S_n=\dfrac{32}{1-0.01}$ Hence, $S_n=\dfrac{3200}{99}$