https://file.aiquickdraw.com/mathbot/file/17261958967527wkrwoa4.jpg

The given expression is a summation:

\[
\sum_{n=0}^{7} (2 + n)^2
\]

This means we need to compute the sum of \((2 + n)^2\) for each integer value of \(n\) from 0 to 7. Let's break it down:

1. For \(n = 0\): \((2 + 0)^2 = 2^2 = 4\)
2. For \(n = 1\): \((2 + 1)^2 = 3^2 = 9\)
3. For \(n = 2\): \((2 + 2)^2 = 4^2 = 16\)
4. For \(n = 3\): \((2 + 3)^2 = 5^2 = 25\)
5. For \(n = 4\): \((2 + 4)^2 = 6^2 = 36\)
6. For \(n = 5\): \((2 + 5)^2 = 7^2 = 49\)
7. For \(n = 6\): \((2 + 6)^2 = 8^2 = 64\)
8. For \(n = 7\): \((2 + 7)^2 = 9^2 = 81\)

Now, summing these values:

\[
4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 = 284
\]

Thus, the value of the summation is:

\[
\sum_{n=0}^{7} (2 + n)^2 = 284
\]

Would you like further details or have any questions?

Here are some related questions:
1. How does summation notation work in general?
2. Can you explain how to handle different types of summations (e.g., arithmetic vs geometric)?
3. What would change in the calculation if the exponent was different, such as \((2 + n)^3\)?
4. How would this summation look if the upper limit were increased to 10?
5. Could this sum be computed using a closed-form formula for summations?

**Tip:** When working with summations, always substitute small values first to get a sense of the pattern before jumping to larger numbers!

Compute the summation: Σ from n=0 to 7 of (2 + n)^2

Solve the summation Σ from n=0 to 7 of (2 + n)^2 with detailed steps, including the expansion of quadratic expressions and summation techniques. Perfect for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation