004 Sample Final A, Problem 13 - Revision history

Kayla Murray at 22:05, 4 May 2015

2015-05-04T22:05:34Z

2015-05-04T21:46:50Z

2015-05-01T04:12:33Z

2015-04-28T22:45:10Z

Created page with "<span class="exam"> Compute <math>\displaystyle{\sum_{n = 1}^6 4\left(\frac{1}{2}\right)^n}</math>"

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<span class="exam"> Compute <math>\displaystyle{\sum_{n = 1}^6 4\left(\frac{1}{2}\right)^n}</math>

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 |Using the above formula, we have
 |-
-|<math>\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}}</math>
+|<math>\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})}</math>
 |}
@@ Line 34: / Line 34: @@
 ! Step 3:
 |-
+|If we simplify, we get
 |-
+|<math>\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}</math>.
 |}
@@ Line 56: / Line 42: @@
 ! Final Answer:
 |-
+|<math>\frac{63}{16}</math>
 |}
 [[004 Sample Final A|<u>'''Return to Sample Exam</u>''']]

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 ! Foundations
 |-
+| What is the formula for the sum of the first n terms of a geometric sequence?
 |-
 |Answer:
 |-
+|The sum of the first n terms of a geometric sequence is <math> S_n=\frac{A_1(1-r^n)}{1-r}</math>
 |}
@@ Line 16: / Line 18: @@
 ! Step 1:
 |-
+|The common ratio for this geometric sequence is <math>r=\frac{1}{2}</math>.
 |-
+|The first term of the geometric sequence is <math>4\frac{1}{2}=2</math>.
 |}
@@ Line 24: / Line 26: @@
 ! Step 2:
 |-
+|Using the above formula, we have
 |}

← Older revision		Revision as of 04:12, 1 May 2015
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	<span class="exam"> Compute <math>\displaystyle{\sum_{n = 1}^6 4\left(\frac{1}{2}\right)^n}</math>		<span class="exam"> Compute <math>\displaystyle{\sum_{n = 1}^6 4\left(\frac{1}{2}\right)^n}</math>
		+	{\| class="mw-collapsible mw-collapsed" style = "text-align:left;"
		+	! Foundations
		+	\|-
		+	\|
		+	\|-
		+	\|Answer:
		+	\|-
		+	\|
		+	\|}
		+
		+
		+	Solution:
		+
		+	{\| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
		+	! Step 1:
		+	\|-
		+	\|
		+	\|-
		+	\|
		+	\|}
		+
		+	{\|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
		+	! Step 2:
		+	\|-
		+	\|
		+	\|}
		+
		+	{\|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
		+	! Step 3:
		+	\|-
		+	\|
		+	\|-
		+	\|
		+	\|-
		+	\|
		+	\|-
		+	\|
		+	\|}
		+
		+	{\|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
		+	! Step 4:
		+	\|-
		+	\|
		+	\|-
		+	\|
		+	\|-
		+	\|
		+	\|}
		+
		+	{\|class = "mw-collapsible mw-collapsed" style = "text-align:left;"
		+	! Final Answer:
		+	\|-
		+	\|
		+	\|}
		+
		+	[[004 Sample Final A\|<u>'''Return to Sample Exam</u>''']]