jmc

A sequence $a_1,$ $a_2,$ $a_3,$ $\dots ,$ is defined recursively by $a_1=1,$ $a_2=1,$ and for $k\ge 3,$ $$a_k=\frac{1}{3}{a}_{k-1}+\frac{1}{4}{a}_{k-2}.$$Evaluate $a_1+a_2+a_3+\cdots .$