Please answer this homework practice and explain in clear, formal, and informative steps. It will be very helpful! Thank you! Define2)-(-)-(-)-(-)-(-)--( - )= 1-f(n)= (1-f(n)= II (1-I(-)-i=21=2where ne Z+ and n ≥ 2.Here, Z+ is the set of all positive integers. Find a rational polynomial that is equal to f(n).=3²Justify this equality by induction.4²(1)

Answered: Define 11 r=II(-5)-(1-5) (-) (--) (--)…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Please answer this homework practice and explain in clear, formal, and informative steps. It will be very helpful! Thank you!

Define
2)-(-)-(-)-(-)-(-)--( - )
= 1-
f(n)= (1-
f(n)= II (1
-I(-)-
i=2
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).
=
3²
Justify this equality by induction.
4²
(1)

Expert Solution

Step 1: Introduction

To find the rational closed form expression for the given partial product $f not stretchy left parenthesis n not stretchy right parenthesis equals product from i equals 2 to n of left parenthesis 1 minus 1 over i squared right parenthesis$ , we can simplify the product using some algebraic manipulations.