The problem asks to evaluate the summation $\sum_{n=9}^{6} (n-1)$. Notice that the upper limit of the summation (6) is smaller than the lower limit (9). In standard summation notation, the lower limit should be smaller than or equal to the upper limit. If the upper limit is smaller than the lower limit, the summation is considered to be zero.

1. Problem Description

The problem asks to evaluate the summation $\sum_{n=9}^{6} (n-1)$. Notice that the upper limit of the summation (6) is smaller than the lower limit (9). In standard summation notation, the lower limit should be smaller than or equal to the upper limit. If the upper limit is smaller than the lower limit, the summation is considered to be zero.

2. Solution Steps

Since the upper limit of the summation is less than the lower limit, the summation is zero.

$$\sum_{n=9}^{6} (n-1) = 0$$

Alternatively, we can reverse the limits of summation and change the sign. Thus,

$$\sum_{n=9}^6 (n-1) = - \sum_{n=6}^9 (n-1)$$

Then, we have

$$- \sum_{n=6}^9 (n-1) = -[(6-1) + (7-1) + (8-1) + (9-1)] = -[5 + 6 + 7 + 8] = -26$$

However, this is incorrect. Since the upper limit is less than the lower limit, we should consider the value to be

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The notation $\sum_{n=a}^b f(n)$ with $b < a$ is often interpreted as

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3. Final Answer

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