/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 30 Find each indicated sum. $$\su... [FREE SOLUTION] | 91影视

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Chapter 8: Problem 30

Find each indicated sum. $$\sum_{i=1}^{6} 7 i$$

Short Answer

Expert verified
The sum \(\sum_{i=1}^{6} 7i\) is 147.

Step by step solution

01

Identify the sum

We recognize this as the sum of the first 6 terms of the arithmetic sequence 7, 14, 21, ..., i.e., \(7 \sum_{i=1}^{6} i\). This is because each term is 7 times the term number.
02

Apply the formula for the sum of the first n natural numbers

Now that the sum has been simplified, apply the formula \(n(n+1)/2\) for the sum of the first n natural numbers, where n = 6. This gives \[7 \times \frac{6(6+1)}{2}\].
03

Calculate the final sum

By carrying out the computation in the expression from step 2, we find the sum. The result is \[7 \times \frac{6 \times 7}{2} = 7^2 \times 6/2 = 21 \times 7 = 147\].

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Most popular questions from this chapter

Exercises \(67-72\) are based on the following jokes about books: \(\cdot\) "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." - Groucho Marx \(\cdot\) "I recently bought a book of free verse. For \(\$ 12\)." \- George Carlin \(\cdot\) "If a word in the dictionary was misspelled, how would we know?" - Steven Wright \(\cdot\) "Encyclopedia is a Latin term. It means 'to paraphrase a term paper." - Greg Ray \(\cdot\) "A bookstore is one of the only pieces of evidence we have that people are still thinking." - Jerry Seinfeld \(\cdot\) "I honestly believe there is absolutely nothing like going to bed with a good book. Or a friend who's read one." \(-\)Phyllis Diller If the order in which these jokes are told makes a difference in terms of how they are received, how many ways can they be delivered if a joke by a man is told first?

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