Define = -ĤI ( ¹ - -¦ ) = (¹ - ¹) · (¹ – ¦ ) · (¹ - -) --- (¹ ---), 1=2 where ne Z+ and n > 2. Here, Z+ is the set of all positive integers. Find a rational polynomial that is equal to f(n). TL f(n) = II (¹-²/1) i=2 = Justify this equality by induction. (1)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Define
f(n)= II (1
= II ( ¹ - ² ) = (¹ - ²¹ ) · ( ¹ − 3 ) · (¹ – ↓ ) --- (¹ - -/-),
-
32
1=2
where n € Z+ and n > 2.
Here, Z+ is the set of all positive integers. Find a rational polynomial that is equal to f(n).
n
ƒ(n) = II (¹-²1)
i=2
=
Justify this equality by induction.
(1)
Transcribed Image Text:Define f(n)= II (1 = II ( ¹ - ² ) = (¹ - ²¹ ) · ( ¹ − 3 ) · (¹ – ↓ ) --- (¹ - -/-), - 32 1=2 where n € Z+ and n > 2. Here, Z+ is the set of all positive integers. Find a rational polynomial that is equal to f(n). n ƒ(n) = II (¹-²1) i=2 = Justify this equality by induction. (1)
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f open parentheses n close parentheses equals product from i equals 2 to n of open parentheses 1 minus 1 over i squared close parentheses

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