Capped doubling payout from tossing until heads

Ken tosses a fair coin repeatedly and stops at the first head. If that happens on toss $k$, he is paid $\min(2^k,64)$ dollars. What is his expected payout?

$7. For $k=1,\dots,6$ each term contributes $2^{-k}\cdot2^k=1$. For $k\ge7$ the payout is capped at $64$, and $P(k\ge7)=2^{-6}$, contributing $1$. Total $6+1=7$.