Problem 93 - Algebra and Trigonometry Real Mathematics, Real People

Question

Find the sum. $$\sum_{k=1}^{4} 10$$

Step-by-Step Solution

Answer

The sum of the series \(\sum_{k=1}^{4} 10\) is \(40\).

Step 1: Understand the sigma notation

Sigma notation provides a way of compactly and precisely expressing any sum, that is, a sequence of things that are all to be added together. The notation itself looks like this: \(\sum_{k=n_1}^{n_2} a_k \). This is simply equal to \(a_{n_1} + a_{n_1+1} + a_{n_1+2} + \cdots + a_{n_2}\). In this exercise, \(\sum_{k=1}^{4} 10\) is the sum of the series and equals \(10 + 10 + 10 + 10\).

Step 2: Summation calculation

Once we understand the sigma notation and what terms we are summing, we simply add these terms together: \(10 + 10 + 10 + 10 = 40\).

Step 3: Final Answer

The sum of the given series \(\sum_{k=1}^{4} 10\) is \(40\).