Find the sum by adding each term together. Use the summation capabilities of a graphing utility to verify your result. Step 1 Use the following property of summation to find the sum Step 2 6 Σ(7i+6) i = 1 Write the sum using the above property. Hence, Σ (a₁ ± b;) = Σa; ± Σ bi 1 = 1 i = 1 i = 1 Step 3 6 6 Σ(7i+6)= Σ i = 1 7 = 1 n i = 1 Since 7 is a constant, use the following property of summation to find the sum Using the above property, / = 1 6 Σ i = 1 = k ka; 6 1 = 1 7i = = Now, find the Σ i = 1 i = 1 7i= 147 6 = 6. a¡ 36 /= 1 (1 + 2 + 7 (21) 147 7 it + X + i = 1 X 6 Ma + i = 1 3+ 4+ 5+ 6) (7i + 6). X + X + 6 Mo i=1 7i-
Find the sum by adding each term together. Use the summation capabilities of a graphing utility to verify your result. Step 1 Use the following property of summation to find the sum Step 2 6 Σ(7i+6) i = 1 Write the sum using the above property. Hence, Σ (a₁ ± b;) = Σa; ± Σ bi 1 = 1 i = 1 i = 1 Step 3 6 6 Σ(7i+6)= Σ i = 1 7 = 1 n i = 1 Since 7 is a constant, use the following property of summation to find the sum Using the above property, / = 1 6 Σ i = 1 = k ka; 6 1 = 1 7i = = Now, find the Σ i = 1 i = 1 7i= 147 6 = 6. a¡ 36 /= 1 (1 + 2 + 7 (21) 147 7 it + X + i = 1 X 6 Ma + i = 1 3+ 4+ 5+ 6) (7i + 6). X + X + 6 Mo i=1 7i-
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![**Finding the Sum of a Series**
To find the sum of the series \(\sum_{i=1}^{6} (7i + 6)\), follow the steps outlined below. Utilize a graphing utility to verify the result if needed.
**Step 1**
Apply the property of summation:
\[
\sum_{i=1}^{n} (a_i \pm b_i) = \sum_{i=1}^{n} a_i \pm \sum_{i=1}^{n} b_i
\]
Rewrite the sum \(\sum_{i=1}^{6} (7i + 6)\) using the above property:
\[
\sum_{i=1}^{6} (7i + 6) = \sum_{i=1}^{6} 7i + \sum_{i=1}^{6} 6
\]
**Step 2**
Since \(7\) is a constant, use the property of summation:
\[
\sum_{i=1}^{n} ka_i = k \sum_{i=1}^{n} a_i
\]
Apply this property to find \(\sum_{i=1}^{6} 7i\):
\[
\sum_{i=1}^{6} 7i = 7 \sum_{i=1}^{6} i
\]
Calculate:
\[
\sum_{i=1}^{6} i = 1 + 2 + 3 + 4 + 5 + 6 = 21
\]
Thus:
\[
7 \times 21 = 147
\]
So:
\[
\sum_{i=1}^{6} 7i = 147
\]
**Step 3**
Now compute \(\sum_{i=1}^{6} 6\):
\[
\sum_{i=1}^{6} 6 = 6 + 6 + 6 + 6 + 6 + 6 = 36
\]
\[
\sum_{i=1}^{6} (7i + 6) = 147 + 36 = 183
\]
The sum of the series is 183.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ba58da1-aa6c-4b34-ac65-53856b97f0bf%2F438139c4-f9c8-42bf-a632-128487076050%2F07q1tp_processed.png&w=3840&q=75)
Transcribed Image Text:**Finding the Sum of a Series**
To find the sum of the series \(\sum_{i=1}^{6} (7i + 6)\), follow the steps outlined below. Utilize a graphing utility to verify the result if needed.
**Step 1**
Apply the property of summation:
\[
\sum_{i=1}^{n} (a_i \pm b_i) = \sum_{i=1}^{n} a_i \pm \sum_{i=1}^{n} b_i
\]
Rewrite the sum \(\sum_{i=1}^{6} (7i + 6)\) using the above property:
\[
\sum_{i=1}^{6} (7i + 6) = \sum_{i=1}^{6} 7i + \sum_{i=1}^{6} 6
\]
**Step 2**
Since \(7\) is a constant, use the property of summation:
\[
\sum_{i=1}^{n} ka_i = k \sum_{i=1}^{n} a_i
\]
Apply this property to find \(\sum_{i=1}^{6} 7i\):
\[
\sum_{i=1}^{6} 7i = 7 \sum_{i=1}^{6} i
\]
Calculate:
\[
\sum_{i=1}^{6} i = 1 + 2 + 3 + 4 + 5 + 6 = 21
\]
Thus:
\[
7 \times 21 = 147
\]
So:
\[
\sum_{i=1}^{6} 7i = 147
\]
**Step 3**
Now compute \(\sum_{i=1}^{6} 6\):
\[
\sum_{i=1}^{6} 6 = 6 + 6 + 6 + 6 + 6 + 6 = 36
\]
\[
\sum_{i=1}^{6} (7i + 6) = 147 + 36 = 183
\]
The sum of the series is 183.
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