kenneth rosen chapter 8 section 8.4 exercise question 5 option (f)

Question

Can anyone explain how to solve part (f) of this question?

It does not seem to fit any standard forms of the generating functions. 

On expanding we get, 4C0+5C1+6C2+7C3+8C4+ …….. inf

 

Answer 1

n-1C0 + nC1 + n+1C2 +.…

= /sum ( n-1+r Cr .X pow r) from r=0to r= infinity

=1/(1-x)pow n

In given question n=5

So,  closed form will be 1/(1-x)pow 5