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robocop_911 June 1st, 2008 04:12 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 05:40 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 06:15 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 10:43 PM

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


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