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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.
\[
S_{4}=
\]
\( \frac{\square}{\square} \)
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Lesson: Geometric mequencas

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Answer

S_4=\frac{15}{4}

Steps

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}

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