Constant terms at each level of a recursion tree In CLRS, exercise 4.4-5 the following question is asked:

Use a recursion tree to determine a good asymptotic upper bound on the recurrence $$T(n) = T(n-1) + T(n/2) + n$$

In my recursion tree, the sum of level 0 is $$n$$ level 1 is $$(3/2)n - 2/2^1$$ level 2 $$(3/2)^2n-14/2^2$$ level 3 is $$(3/2)^3n - 74/2^3$$
and so on. My issues is that the rule governing the constants 2, 14, 74 etc. is difficult to express as a function of the level so that I can create a sum for all levels of the tree.
Would it be correct to say that the cost at each level of the tree is $$(3/2)^in - O(1)$$
and thus avoid the problem of having to sum all of the constant terms via big O notation, or is this approach incorrect? If so, why and what should I do instead?
For each specific level $i$, it is true that the cost is $(3/2)^i n - O(1)$. However it would be misleading to state this in general. Suppose for example that the cost at level $i$ were $(3/2)^i n + 2^{2^i}$, and that there were $\log n$ levels. The dominant factor in the total cost would be the &quot;constant&quot; term.
However, in your case, you can say that the cost at level $i$ is at most $(3/2)^i$, which gives you the required upper bound.