23. > i(i + 3)² i= 1 THEOREM 4.2 Summation Formulas n(n + 1) п п 1. >c = cn, c is a constant 2. S i=1 i=1 n(n + 1)(2n + 1) 6. n2(n + 1)2 п 3. Si? 4. 4 i=1 A proof of this theorem is given in Appendix A. CONCEPT CHECK 1. Sigma Notation What are the index of summation, the upper bound of summation, and the lower bound of summation for (i – 4)? 2. Sums What is the value of n? 5(5 + 1) 20(20 + 1)[2(20) + 1] п (a) E (b) 3. Upper and Lower Sums In your own words and using appropriate figures, describe the methods of upper sums and lower sums in approximating the area of a region. 4. Finding Area by the Limit Definition Explain how to find the area of a plane region using limits.
23. > i(i + 3)² i= 1 THEOREM 4.2 Summation Formulas n(n + 1) п п 1. >c = cn, c is a constant 2. S i=1 i=1 n(n + 1)(2n + 1) 6. n2(n + 1)2 п 3. Si? 4. 4 i=1 A proof of this theorem is given in Appendix A. CONCEPT CHECK 1. Sigma Notation What are the index of summation, the upper bound of summation, and the lower bound of summation for (i – 4)? 2. Sums What is the value of n? 5(5 + 1) 20(20 + 1)[2(20) + 1] п (a) E (b) 3. Upper and Lower Sums In your own words and using appropriate figures, describe the methods of upper sums and lower sums in approximating the area of a region. 4. Finding Area by the Limit Definition Explain how to find the area of a plane region using limits.
"Evaluating a Sum". Use the properties of summation and Theorem 4.2 to evaluate the sum. Use the summation capabilities of a graphing utility to verify your result. Please show work and explain steps.
Transcribed Image Text:23. > i(i + 3)²
i= 1
Transcribed Image Text:THEOREM 4.2 Summation Formulas
n(n + 1)
п
п
1.
>c = cn, c is a constant
2. S
i=1
i=1
n(n + 1)(2n + 1)
6.
n2(n + 1)2
п
3. Si?
4.
4
i=1
A proof of this theorem is given in Appendix A.
CONCEPT CHECK
1. Sigma Notation
What are the index of summation,
the upper bound of summation, and the lower bound of
summation for (i – 4)?
2. Sums What is the value of n?
5(5 + 1)
20(20 + 1)[2(20) + 1]
п
(a) E
(b)
3. Upper and Lower Sums In your own words and
using appropriate figures, describe the methods of upper
sums and lower sums in approximating the area of a region.
4. Finding Area by the Limit Definition Explain
how to find the area of a plane region using limits.
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![THEOREM 4.2 Summation Formulas
n(n + 1)
п
п
1.
>c = cn, c is a constant
2. S
i=1
i=1
n(n + 1)(2n + 1)
6.
n2(n + 1)2
п
3. Si?
4.
4
i=1
A proof of this theorem is given in Appendix A.
CONCEPT CHECK
1. Sigma Notation
What are the index of summation,
the upper bound of summation, and the lower bound of
summation for (i – 4)?
2. Sums What is the value of n?
5(5 + 1)
20(20 + 1)[2(20) + 1]
п
(a) E
(b)
3. Upper and Lower Sums In your own words and
using appropriate figures, describe the methods of upper
sums and lower sums in approximating the area of a region.
4. Finding Area by the Limit Definition Explain
how to find the area of a plane region using limits.](https://content.bartleby.com/qna-images/question/f929f9c5-3173-423c-ac83-e2c455140904/01ede1e6-6877-417a-a8a4-b865a69e1342/tb3rzg.jpeg)
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