Solving a simple recurrence I'm having a real hard time solving recurrences using the substitution method.

Show that: $T(n) = T(n/2) + 1$ is $O(\lg n)$

I thought this to be relatively easy:

We have to show that $T(n) \leq c \lg n$

Substitution gives me:

$\qquad
  \begin{align}
    T(n) &amp;\leq c \lg(n/2) + 1 \\
         &amp;= c \lg n - c \lg 2 + 1 \\
         &amp;= c \lg n - c + 1 \\
         &amp;\leq  c \lg n
\end{align}$ 

for every c.

I was under the impression this was it, but when I was looking for an answer, I came around a much more elaborate answer on the web, given  involving subtracting a constant. I don't get why that's needed, I thought I had shown what was needed.

Any help would be greatly appreciate, starting Monday I'm enrolled in an algorithms class and I don't want to get behind!

We are using the CLRS book (surprise) and though I appreciate the amount of information in it, I'd rather have some more resources. I've really enjoyed a datastructures class and I really think I can enjoy this as well, but more resources would be very much appreciated.
Luckily i had 2 day ago the algorithm exam and so i was able to solve your question :-)
When solving recurrences try first to use the Master method, if you can't succeed than try other methods.