Compute 
| Foundations
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| What is the formula for the sum of the first n terms of a geometric sequence?
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| Answer:
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The sum of the first n terms of a geometric sequence is 
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where  is the common ratio and  is the first term of the geometric sequence.
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Solution:
| Step 1:
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| The common ratio for this geometric sequence is Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle r={\frac {1}{2}}}
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| The first term of the geometric sequence is Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 4{\frac {1}{2}}=2}
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| Step 2:
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| Using the above formula, we have
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| Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \displaystyle {\sum _{n=1}^{6}4\left({\frac {1}{2}}\right)^{n}}=S_{6}={\frac {2(1-({\frac {1}{2}})^{6})}{(1-{\frac {1}{2}})}}}
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| Step 3:
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| If we simplify, we get
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| Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \displaystyle {\sum _{n=1}^{6}4\left({\frac {1}{2}}\right)^{n}}={\frac {2(1-{\frac {1}{64}})}{\frac {1}{2}}}=4{\frac {63}{64}}={\frac {63}{16}}}
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| Final Answer:
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| Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\frac {63}{16}}}
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