Sum of nth bracket sequence:

To find the sum of the nth bracket sequence, we need to understand the pattern and calculate the sum for each bracket individually. Let's break down the given sequence and calculate the sum step by step.

The given sequence is: (1) (2 3 4) (5 6 7 8 9)

Step 1: Identify the brackets:
The given sequence consists of three brackets: (1), (2 3 4), and (5 6 7 8 9).

Step 2: Calculate the sum of each bracket:
Now, we will calculate the sum of each bracket individually.

Bracket 1: (1)
This bracket has only one element, which is 1. Therefore, the sum of this bracket is 1.

Bracket 2: (2 3 4)
This bracket has three elements: 2, 3, and 4. To find the sum, we add these numbers together: 2 + 3 + 4 = 9.

Bracket 3: (5 6 7 8 9)
This bracket has five elements: 5, 6, 7, 8, and 9. Adding these numbers together gives us the sum: 5 + 6 + 7 + 8 + 9 = 35.

Step 3: Calculate the sum of the entire sequence:
To find the sum of the entire sequence, we add the sums of each bracket together.

Sum of (1) + (2 3 4) + (5 6 7 8 9) = 1 + 9 + 35 = 45.

Therefore, the sum of the given sequence is 45.

Summary:
The given sequence consists of three brackets: (1), (2 3 4), and (5 6 7 8 9). The sum of each bracket is calculated separately by adding the elements within each bracket. Finally, the sums of all the brackets are added together to obtain the sum of the entire sequence, which is 45.