1 Σ1 п+1 k=0 n 2 Σ п(п+1) 2 k=0 n 3 Σ п(п+1)(2п+1) k=0 n Σ 3 n²(n+1)² 4 4. k=0
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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Explain the determaine
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Difference Equations
TABLE 1.2:
Definite Sums of Selected Functions
Number Summation
Definite Sum
1
Σ1
n +1
k=0
n
2
k
n(n+1)
k=0
n
3
п(п+1)(2п+1)
k=0
E k3
n?(n+1)²
4
k=0
E k(m), m # –1
(n+1)(m+1)
т+1
k=0
[a(п+1)+b(т+1)_ь(m+1)
а(m+1)
n
6
E (ak + b)(m), m + -1
k=0
n+1_1
7
Σ α, α1
а—1
k=0
Itu
(а-1)(п+1)а"+1-а'
n+2
+a
E kak, a + 1
(а-1)2
k=0
п
E sin(ak), a + 2mT
cos{a[(n+1)/2]} cos(an/2)
sin(a/2)
9
k=0
n
Σ cos(ak), a # 2mπ
sin{a[(n+1)/2]} cos(an/2)
sin(a/2)
10
k=0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F24d8083d-2f6b-4b3a-ae37-f1d832402efe%2Faf505dfe-b3cd-4731-bcc9-8886a0d10fd4%2Fv06vxl8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:34
Difference Equations
TABLE 1.2:
Definite Sums of Selected Functions
Number Summation
Definite Sum
1
Σ1
n +1
k=0
n
2
k
n(n+1)
k=0
n
3
п(п+1)(2п+1)
k=0
E k3
n?(n+1)²
4
k=0
E k(m), m # –1
(n+1)(m+1)
т+1
k=0
[a(п+1)+b(т+1)_ь(m+1)
а(m+1)
n
6
E (ak + b)(m), m + -1
k=0
n+1_1
7
Σ α, α1
а—1
k=0
Itu
(а-1)(п+1)а"+1-а'
n+2
+a
E kak, a + 1
(а-1)2
k=0
п
E sin(ak), a + 2mT
cos{a[(n+1)/2]} cos(an/2)
sin(a/2)
9
k=0
n
Σ cos(ak), a # 2mπ
sin{a[(n+1)/2]} cos(an/2)
sin(a/2)
10
k=0
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