Find the sum of the finite series.
9
∑
n=0
41

The series you've given is a summation from \( n = 0 \) to \( n = 9 \) of the constant value 41. This is a finite arithmetic series where each term is 41.

The sum of a constant series is calculated as:

\[
S = c \times (n_{\text{end}} - n_{\text{start}} + 1)
\]

Where:
- \( c = 41 \) (the constant value of each term),
- \( n_{\text{start}} = 0 \),
- \( n_{\text{end}} = 9 \).

Thus, the number of terms in the series is \( n_{\text{end}} - n_{\text{start}} + 1 = 9 - 0 + 1 = 10 \).

Now, calculate the sum:

\[
S = 41 \times 10 = 410
\]

So, the sum of the finite series is \( 410 \).

Would you like further explanation or have any questions?

Here are 5 related questions to extend this concept:
1. How do you find the sum of an arithmetic series where the terms vary?
2. What is the formula for the sum of a geometric series?
3. How do you calculate the sum of a series with both positive and negative terms?
4. What is the sum of the series if the constant value changes to 50?
5. How do you generalize the sum of a series with a constant?

**Tip:** When dealing with summation of constant values, always check the range to easily multiply by the number of terms.

Find the sum of the finite series: 9 ∑ n=0 41

Learn how to find the sum of the finite series 9 ∑ n=0 41. This example explains the calculation of a constant series, where each term equals 41. The step-by-step solution uses the formula for summing a constant value over a given range. Perfect for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation