Use sigma notation to write the sum. [2((1)/(8))+3]+[2((2)/(8))+3]+⋯+[2((8)/(8))+3]

Name: Problem 81, Chapter 8: College Algebra
Uploaded: 2021-10-15T22:03:55-08:00
Duration: 1 min 13 s
Channel: James Kiss
Description: Use sigma notation to write the sum. [2((1)/(8))+3]+[2((2)/(8))+3]+⋯+[2((8)/(8))+3]

step 1 If we were adding 2 times 1 eighth plus 3 with 2 times 2 8ths plus 3 plus all the way to 2 times

Question

Use sigma notation to write the sum. $$\left[2\left(\frac{1}{8}\right)+3\right]+\left[2\left(\frac{2}{8}\right)+3\right]+\cdots+\left[2\left(\frac{8}{8}\right)+3\right]$$

   Use sigma notation to write the sum.
$$\left[2\left(\frac{1}{8}\right)+3\right]+\left[2\left(\frac{2}{8}\right)+3\right]+\cdots+\left[2\left(\frac{8}{8}\right)+3\right]$$

College Algebra

Ron Larson 9th Edition

Chapter 8, Problem 81

Instant Answer

Solved by Expert James Kiss

10/15/2021

Step 1

This is the pattern that we can use to write the sum in sigma notation. Show more…

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Use sigma notation to write the sum. $$\left[2\left(\frac{1}{8}\right)+3\right]+\left[2\left(\frac{2}{8}\right)+3\right]+\cdots+\left[2\left(\frac{8}{8}\right)+3\right]$$

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Key Concepts

Sigma Notation

Sigma notation is a concise way of writing sums of sequences by using the symbol ?. It describes the sum of terms defined by a function of an index variable over a specific range. Sigma notation simplifies the representation of long sums by indicating the variable's starting and ending values and the general term to be summed.

Indexing in Summation

Indexing involves the use of an index variable, often denoted as 'k' or 'i', which takes on successive integer values and is used to generate each term in the series. Proper indexing defines the lower and upper limits of the sum and ensures each term is accounted for in the series.

Representation of General Terms

In summing sequences, representing each term as a function of the index variable allows for generalization and simplifies the expression of the sum. This concept is crucial when rewriting a series of terms in sigma notation, as it enables one to express the pattern in a compact mathematical form.

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