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Chapter 9: Problem 93

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

Short Answer

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

Step by step solution

01

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 \(10 + 10 + 10 + 10\).
02

Summation calculation

Once we understand the sigma notation and what terms we are summing, we simply add these terms together: \(10 + 10 + 10 + 10 = 40\).
03

Final Answer

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

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Most popular questions from this chapter

Write an expression for the apparent \(n\) th term of the sequence. (Assume \(n\) begins with \(1 .\)) $$\frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \frac{5}{6}, \frac{6}{7}, \dots$$

Find the indicated term of the sequence. $$\begin{aligned} &a_{n}=(-1)^{n-1}[n(n-1)]\\\ &a_{16}= \end{aligned}$$

Find the indicated term of the sequence. $$\begin{aligned} &a_{n}=\frac{3^{n}}{3^{n}+1}\\\ &a_{6}= \end{aligned}$$

Use a graphing utility to find the partial sum. $$\sum_{n=1}^{50}(40-2 n)$$

Write the first five terms of the sequence (a) using the table feature of a graphing utility and (b) algebraically. (Assume \(n\) begins with 0.) $$a_{n}=\frac{(-1)^{2 n+1}}{(2 n+1) !}$$
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