Combo Identity: How to prove this using Induction 
$$ \sum_{n = 0}^{\infty} \binom{n + k}{k}x^n = \dfrac{1}{(1 - x)^{k + 1}} $$

Could someone suggest how I should get started to prove this using induction?

HINT:
$$\frac1{(1-x)^{m+1}}=\frac{1-x}{(1-x)^{m+2}}=\frac1{(1-x)^{m+2}}-\frac x{(1-x)^{m+2}}$$
$$\implies(1-x)^{-(m+1)}=(1-x)^{-(m+2)}-x(1-x)^{-(m+2)}$$
Assume that the formula is true for $k=m+2$ and establish the same for $k=m+1$

Alternatively, use  $$(1-x)(1-x)^{-(m+2)}=(1-x)^{-(m+1)}$$
Assume that the formula is true for $k=m+1$ and establish the same for $k=m+2$
