Evaluating the generating function

Asked Jun 06 '21 at 20:58

Active Jun 06 '21 at 20:58

Viewed 27 times

From yesterday I've stucked with the following problem from my class homework

Find the generating function $$ \sum_{n=0}^{\infty} \binom{n+k-1}{n} \cdot x^n $$

I've tried several different approaches, but none of them worked here. So, I don't know how to even make the first step to solution.

Any hints/ideas would be very appreciated.

asked Jun 06 '21 at 20:58

Levon Minasian

1

What is it when $k=1?$ $k=2?$ – Thomas Andrews Jun 06 '21 at 21:01
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$k=1$ implies that this is $1/(1-x)$ – Levon Minasian Jun 06 '21 at 21:02
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$k=2$ implies $1/(1-x)^2$ !!! – Levon Minasian Jun 06 '21 at 21:06
I'll try the induction. Thanks for the idea – Levon Minasian Jun 06 '21 at 21:06
@Sil Yep, you got it right – Levon Minasian Jun 07 '21 at 12:41

0 Answers0