calculate-n-p-C-n-p-x-n-

Question Number 28620 by abdo imad last updated on 28/Jan/18

c a l c u l a t e \sum_{n = p}^{+ \infty} C_{n}^{p} x^{n} .

Commented by Tinkutara last updated on 28/Jan/18

H o w c a n n > p b e c a s u c e i t i s u s e d i n

^{p} C_{n} ?

Commented by abdo imad last updated on 28/Jan/18

\sum_{n = p}^{\propto} C_{n}^{p} x^{n} = C_{p}^{p} x^{p} + C_{p + 1}^{p} x^{p + 1} + \dots

Commented by Tinkutara last updated on 28/Jan/18

B u t w h a t i s^{p} C_{p + 1} ? I s i t c o m b i n a t i o n ?

B e c a u s e i f w e w r i t e^{n} C_{r} i t m e a n s

r ⩽ n .

Commented by abdo imad last updated on 28/Jan/18

f o r u s w e u s e C_{n}^{p} = \frac{n!}{p! (n - p)!} f o r p ⩽ n i t s o n l y a n o t a t i o n

o f c o m b i n a t i o n . .