Capped doubling payout from coin tosses

Samuel tosses a fair coin until the first tail appears; let $n$ be the total number of tosses, including that tail. He is then paid $\min(64,2^n)$ dollars. What is his expected payout?

$7. For $n\le 5$ the payout $2^n$ has probability $2^{-n}$, contributing $1 each, so $5 in total. The cap of $64 applies when $n\ge 6$, which has probability $2^{-5}$, adding $64/32=$ $2.