Problem
Math Recommendations Skill plans CC.19 Partial sums of geometric series 9JU Find the fourth partial sum of the series. \[ 2+1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\cdots \] Write your answer as an integer or a fraction in simplest form. \[ S_{4}= \] \( \frac{\square}{\square} \) Submit Work it out Not feeling ready yet? These Introduction to partial sums Lesson: Geometric mequencas
Solution
Step 1 ：S_4=2+1+\frac{1}{2}+\frac{1}{4}
Step 2 ：\frac{a_1(1-r^n)}{1-r}
Step 3 ：\frac{2(1-(\frac{1}{2})^4)}{1-\frac{1}{2}}
Step 4 ：S_4=\frac{15}{4}
