i n-i = (x+ y) ". п i=0 Use this to prove that: 3 (i) n п — 1 п — -2 n 2 + n n |2+ 1 n 1 2 |2 + + ... n [Hint: Consider writing 3 as the sum of two integers, x + y.]
i n-i = (x+ y) ". п i=0 Use this to prove that: 3 (i) n п — 1 п — -2 n 2 + n n |2+ 1 n 1 2 |2 + + ... n [Hint: Consider writing 3 as the sum of two integers, x + y.]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Recall that the binomial theorem states:
![n
i n-i
(:)
n
x 'y
i
= (x + y) ".
i=0
n
Use this to prove that: 3 =
п —1
(4):
(:)
п
п
2 +
n
|2
2
п
п
п
2
+
+ ... +
|2+
1
1
n
[Hint: Consider writing 3 as the sum of two integers, x + y.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd15c165e-39ef-478b-a90f-b8114f0d2e93%2Ff3c38f93-7929-4a8b-9de9-fa836fe1e275%2F8yild2r_processed.png&w=3840&q=75)
Transcribed Image Text:n
i n-i
(:)
n
x 'y
i
= (x + y) ".
i=0
n
Use this to prove that: 3 =
п —1
(4):
(:)
п
п
2 +
n
|2
2
п
п
п
2
+
+ ... +
|2+
1
1
n
[Hint: Consider writing 3 as the sum of two integers, x + y.]
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