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 robocop_911 June 1st, 2008 03:12 PM

"Recursive definition"

Can anyone give "recursive" definition of the sequences given below?
n = 1,2,3...

Code:

```a) a_n = 4n-2 b) a_n = 1 + (-1)^n c) a_n = n(n+1) d) a_n = n^2```
Thanks for any quick help!
Please provide me with explanation too!

Also, is there any LaTeX in this forum?

 CRGreathouse June 1st, 2008 04:40 PM

If you write out a_n - a_(n-1), you'll find the recursive forms fairly easily. For the first, a_n - a_(n-1) = (4n - 2) - (4(n-1) - 2) = 4, so a_n = a_(n-1) + 4.

LaTeX is coming soon!

 robocop_911 June 1st, 2008 05:15 PM

Quote:
 Originally Posted by CRGreathouse If you write out a_n - a_(n-1), you'll find the recursive forms fairly easily. For the first, a_n - a_(n-1) = (4n - 2) - (4(n-1) - 2) = 4, so a_n = a_(n-1) + 4. LaTeX is coming soon!
Code:

```Is this true for 2nd one... a_n - a_n-1 = 2 (-1)^n Is this recursive definition correct? for question b)```

 CRGreathouse June 1st, 2008 09:43 PM

No. (-1)^n - (-1)^(n-1) is either 2 or -2. a_n + a_(n-1) = 0.

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