Chapter 12 Sequences and Series - 12.4 Find Sums of Infinite Geometric Series - 12.4 Exercises - Skill Practice - Page 823: 4

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Here we have $S_1=\dfrac{2}{3}=0.67; \\S_2=\dfrac{2}{3}+\dfrac{1}{3}=1 ; \\S_3=\dfrac{2}{3}+\dfrac{1}{3}+\dfrac{1}{6}=1.167 ; \\S_4=\dfrac{2}{3}+\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{12}=1.25 ; \\ S_5=\dfrac{2}{3}+\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{24}=1.29$. Thus, as $n$ increases $S_n$ also increases, and the value approaches $1.33$ as $n \to \infty$