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The identity formula we have been using is 1/n= 1/(n+1) + 1/n(n+1).  Here is the problem at hand: Let n be a positive off integer number (i.e. n=2k+1, for some integer k). Find a unit fraction representation of 3/n consisting of three terms. Express the unit representation in terms of n and k in simplest form. I don't know how to find the extra third term. I wrote this so far 3/(2k+1) = 3/(2k+2) + 3/(2k+1)(2k+2) +

The identity formula we have been using is 1/n= 1/(n+1) + 1/n(n+1).  Here is the problem at hand: Let n be a positive off integer number (i.e. n=2k+1, for some integer k). Find a unit fraction representation of 3/n consisting of three terms. Express the unit representation in terms of n and k in simplest form. I don't know how to find the extra third term. I wrote this so far 3/(2k+1) = 3/(2k+2) + 3/(2k+1)(2k+2) +

Advanced Engineering Mathematics
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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The identity formula we have been using is 1/n= 1/(n+1) + 1/n(n+1). 

Here is the problem at hand:

Let n be a positive off integer number (i.e. n=2k+1, for some integer k). Find a unit fraction representation of 3/n consisting of three terms. Express the unit representation in terms of n and k in simplest form.

I don't know how to find the extra third term. I wrote this so far 3/(2k+1) = 3/(2k+2) + 3/(2k+1)(2k+2) + ?

Expert Solution
Step 1

We need to use given identity twice to represent the unit fraction  in three term 

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