# How do give the recursive form for a certain function?

• October 23rd 2009, 03:13 AM
thename1000
How do give the recursive form for a certain function?
I only have the explanation for linear homogeneous ones. I don't know how to do these:

Give a recursive form (including bases) for the following functions:
a. f(n) = 2 + (-1)^n
b. f(n) = n(n+1)
c. f(n) = 2n - 2
d. f(n) = n^2 – n
e. f(n) = 3^n + n⋅3^n

If someone could explain one or two it would help alot.

Thanks
• October 23rd 2009, 02:37 PM
CaptainBlack
Quote:

Originally Posted by thename1000
I only have the explanation for linear homogeneous ones. I don't know how to do these:

Give a recursive form (including bases) for the following functions:
a. f(n) = 2 + (-1)^n

$f(n)-f(n-1)=(-1)^n-(-1)^{n-1}=(-1)^n+(-1)^n=2 (-1)^n$

and take it from there

CB
• October 23rd 2009, 02:44 PM
CaptainBlack
Quote:

Originally Posted by thename1000
I
d. f(n) = n^2 – n

$f(n)=n^2-n$

$f(n-1)=n^2-3n+2$

$f(n-2)=n^2-5n+4$

so:

$f(n-2)-2f(n-1)=(n^2-5n+4)-2(n^2-3n+2)=-n^2+n=-f(n)$

CB