To solve the problem in question 1, we need to calculate the value of the summation:

$\sum_{n=-2}^{2} (n^2 - 3n)$

This requires us to evaluate the expression $n^2 - 3n$ for each integer value of $n$ from $-2$ to $2$, and then sum the results.

Step-by-Step Solution

1. Calculate each term in the summation:

   • For $n = -2$: $(-2)^2 - 3(-2) = 4 + 6 = 10$
   • For $n = -1$: $(-1)^2 - 3(-1) = 1 + 3 = 4$
   • For $n = 0$: $0^2 - 3 \cdot 0 = 0$
   • For $n = 1$: $1^2 - 3 \cdot 1 = 1 - 3 = -2$
   • For $n = 2$: $2^2 - 3 \cdot 2 = 4 - 6 = -2$

2. Sum the results: $10 + 4 + 0 - 2 - 2 = 10$

Final Answer

The value of the summation is: $\sum_{n=-2}^{2} (n^2 - 3n) = 10$

Would you like further details on any part of this solution?

Related Questions:

1. How do you calculate a general summation formula for any given range?
2. What if the expression inside the summation was different, such as $n^3 - 2n$?
3. How can summation be applied to solve real-world problems in statistics?
4. Can we use sigma notation for non-integer values of $n$?
5. What is the difference between finite and infinite summations?

Tip:

Always break down each term in a summation individually before summing them, especially when working with expressions involving both $n$ and $n^2$.