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Chapter 8: Problem 29

Find each indicated sum. $$\sum_{i=1}^{6} 5 i$$

Short Answer

Expert verified
The result is 105.

Step by step solution

01

Understand the Sigma Notation

The problem provides a sum in sigma notation, written as \(\sum_{i=1}^{6} 5i\). The 'i=1' underneath the sigma indicates that the first term of the sum is when i = 1, and the '6' above sigma indicates that the last term of the sum is when i = 6.
02

Write out the Sequence

According to the information provided, the sequence can be written out as: \(5*1, 5*2, 5*3, 5*4, 5*5, 5*6\).
03

Calculate each Term of the Sequence

The sequence becomes: 5, 10, 15, 20, 25, 30.
04

Sum up all the Terms

The sum of all the terms in the sequence is: \(5+10+15+20+25+30=105\).

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Most popular questions from this chapter

Enough curiosities involving the Fibonacci sequence exist to warrant a flourishing Fibonacci Association, which publishes a quarterly journal. Do some research on the Fibonacci sequence by consulting the Internet or the research department of your library, and find one property that interests you. After doing this research, get together with your group to share these intriguing properties.

Write the first three terms in each binomial expansion, expressing the result in simplified form. $$ \left(x^{2}+1\right)^{17} $$

Use the Binomial Theorem to expand each binomial and express the result in simplified form. $$ (y-3)^{4} $$

Explain how to find the general term of a geometric sequence.

Find the term indicated in each expansion. \(\left(x+\frac{1}{2}\right)^{8} ;\) fourth term
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