Chapter 12 Sequences and Series - 12.3 Analyze Geometric Sequences and Series - 12.3 Exercises - Skill Practice - Page 815: 51

$S_6=\dfrac{1365}{256} \approx 5.332$

Here, we have $\sum_{i=1}^6 4(1/4)^{i-1}$ We know that $S_{n}=a_1(\dfrac{1-r^{n}}{1-r})$ Now, $S_6=4[\dfrac{1-(1/4)^{6}}{1-(1/4)}]$ or, $=4 \times (\dfrac{4096/4096-1/4096}{3/4})$ or, $=4 \times \dfrac{1365}{1024}$ Hence, $S_6=\dfrac{1365}{256} \approx 5.332$