In order to present \$e^x+y=e^xe^y\$ by making use of Exponential Series, I obtained the following:

\$\$e^xe^y=Big(sum_n=0^inftyx^n over n!Big)cdot Big(sum_n=0^inftyy^n over n!Big)=sum_n=0^inftysum_k=0^nx^ky^n over k!n!\$\$

But, where must I go beside get \$e^x+y=sum_n=0^infty(x+y)^n over n!\$.