Closed form solution for recurrence I need to find a closed form solution for the following recurrence:
$T(m) \leq T(\sqrt m) + 1$, $T(1)=1$
I honestly don't have even have an idea where to start. Help would be greatly appreciated!

$$T(m^{2^{0}})-T(m^{2^{-1}})\leq 1$$
$$T(m^{2^{-1}})-T(m^{2^{-2}})\leq 1$$
$$.$$
$$.$$
$$.$$
$$T(m^{2^{-(n-1)}})-T(m^{2^{-n}})\leq 1$$
Add all inequalities (notice that the sum in the LHS is telescoping):
$$T(m)-T(m^{2^{-n}})\leq n$$
$$T(m)-n\leq T(m^{2^{-n}})$$
