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Exercise 4.5 (one of the simple ones)
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Joined: 26 Mar 2008, 17:06
Posts: 2
Exercise 4.5 (one of the simple ones)
Can someone help me with exercise 4.5, which asks about an elementary reason for the simple relationship between the two following power series:
1) 1 + x^2 + x^4 + x^6 ...
2) 1 - x^2 + x^4 - x^6

26 Mar 2008, 17:10

Joined: 26 Mar 2008, 21:50
Posts: 1
Re: Exercise 4.5 (one of the simple ones)
yeah i couldnt figure that out too

26 Mar 2008, 21:54

Joined: 12 Mar 2008, 10:57
Posts: 69
Location: India
Re: Exercise 4.5 (one of the simple ones)

This would suffice.

01 Apr 2008, 06:44

Joined: 22 Jan 2009, 19:33
Posts: 2
Re: Exercise 4.5 (one of the simple ones)
Sameedâ€™s solution is perfect, but it was no evident to me. So I developed it:

etc.

In general:

etc.

Now we have:

Perhaps this could be helpful for any other.

Manuel

27 Jan 2009, 18:53

Joined: 09 Jan 2010, 02:06
Posts: 1
Re: Exercise 4.5 (one of the simple ones)
Here's another one, not as easy as Sameed's but still elementary:

Change to get

Now multiply both sides by :

Multiplying the RHS of the equation:

Finally, rearranging:

This solution doesn't use complex numbers, which are introduced later in the book

14 Feb 2010, 03:39
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