Summation with Kronecker delta

Question

I am having some trouble in understading why $$\sum_{m=0}^{\infty} e^{mix}\delta_{k+m} = e^{-ikx}$$ which was the result i got from wolfram

Answer 1

Since the kronecker delta $\delta[n]$ is non zero only when $n=0$ and $0$ for all other $n\neq 0$. No term other than $k+m=0$ ie $m=-k$ contributes in the sum and the sum collapses to $e^{i(-k)x}=e^{-ikx}$.