The alternative? Learn to love recursion trees. It addresses both issues. It's intuitive and it's general. As a side effect, the master theorem becomes an almost obvious fact; the three different cases correspond to geometric sums with increasing, decreasing and constant terms, with the caveat that since we are working asymptotically, increasing/decreasing/constant must be interpreted in the looser asymptotic sense. A geometric series with increasing (decreasing) terms is dominated by its last (first) term, corresponding in the recursion to the last (first) level of the tree. That makes it trivial to estimate the sum: just estimate the cost at the appropriate level and you're done. Only in the constant term case do all the terms play a role, but then you get your estimate by just multiplying the number of terms (the tree depth) by the constant value the terms have in common.