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The equation below is intuitively correct, but how do you show that this is actually the case? What is the working out needed?

$$\sum_{i=1}^{n-1}O(\log n)=O(n\lg n)$$$$\sum_{i=1}^{n-1}O(\lg n)=O(n\lg n)$$

The equation below is intuitively correct, but how do you show that this is actually the case? What is the working out needed?

$$\sum_{i=1}^{n-1}O(\log n)=O(n\lg n)$$

The equation below is intuitively correct, but how do you show that this is actually the case? What is the working out needed?

$$\sum_{i=1}^{n-1}O(\lg n)=O(n\lg n)$$

The equation below is intuitively correct, but how do you show that this is actually the case? What is the working out needed? $$\sum_{i=1}^{n-1}O(lg n) = O(nlgn)$$

$$\sum_{i=1}^{n-1}O(\log n)=O(n\lg n)$$

The equation below is intuitively correct, but how do you show that this is actually the case? What is the working out needed? $$\sum_{i=1}^{n-1}O(lg n) = O(nlgn)$$

The equation below is intuitively correct, but how do you show that this is actually the case? What is the working out needed?

$$\sum_{i=1}^{n-1}O(\log n)=O(n\lg n)$$

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How to show working for summing of Big O notation

The equation below is intuitively correct, but how do you show that this is actually the case? What is the working out needed? $$\sum_{i=1}^{n-1}O(lg n) = O(nlgn)$$