Leftist Tree initialization in O(n) time
The succession $a_i = 2^{-i}i$ is absolutely convergent.

In more elementary terms:

$$
\frac{n}{2} \le \sum_{i=1}^{\log n} \frac{ni}{2^i} \le n\sum_{i=1}^{\infty} \frac{i}{2^i} = n\sum_{j=1}^{\infty} \left( \frac{1}{2^j}\sum_{i=1}^{\infty}  \frac{1}{2^i} \right) = 2n
$$