Q 57. In Problems 51鈥�60, write out e... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 12: Q 57. (page 809)

In Problems 51鈥�60, write out each sum.
${鈭�}_{k = 0}^{n - 1} \frac{1}{3^{k + 1}}$

Short Answer

Expert verified

The required sum is ${鈭�}_{k = 0}^{n - 1} \frac{1}{3^{k + 1}} = \{\frac{1}{3} + \frac{1}{9} + \frac{1}{27} + . . . . . . + \frac{1}{3^{n}}\}$ .

Step by step solution

Step 1. Write the given information.

The given summation notation is:

${鈭�}_{k = 0}^{n - 1} \frac{1}{3^{k + 1}}$

Step 2. Write out the sum.

To get the sum, we need to substitute $0, 1, 2, . . . . . . . ., n - 1$ for k,in the given sequence ${鈭�}_{k = 0}^{n - 1} \frac{1}{3^{k + 1}}$ ,

${鈭�}_{k = 0}^{n - 1} \frac{1}{3^{k + 1}} = \{\frac{1}{3^{0 + 1}} + \frac{1}{3^{1 + 1}} + \frac{1}{3^{2 + 1}} + . . . . . . + \frac{1}{3^{n - 1 + 1}}\} = \{\frac{1}{3} + \frac{1}{3^{2}} + \frac{1}{3^{3}} + . . . . . . + \frac{1}{3^{n}}\} = \{\frac{1}{3} + \frac{1}{9} + \frac{1}{27} + . . . . . . + \frac{1}{3^{n}}\}$

Therefore, ${鈭�}_{k = 0}^{n - 1} \frac{1}{3^{k + 1}} = \{\frac{1}{3} + \frac{1}{9} + \frac{1}{27} + . . . . . . + \frac{1}{3^{n}}\}$ .

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91影视

In Problems 51鈥�60, write out each sum.
${鈭�}_{k = 0}^{n - 1} \frac{1}{3^{k + 1}}$

Short Answer

Step by step solution

Step 1. Write the given information.

Step 2. Write out the sum.

One App. One Place for Learning.

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91影视

In Problems 51鈥�60, write out each sum.鈭�k=0n-113k+1

Short Answer

Step by step solution

Step 1. Write the given information.

Step 2. Write out the sum.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Geometry

Logic and Functions

Mechanics Maths

Probability and Statistics

Calculus

Study anywhere. Anytime. Across all devices.

In Problems 51鈥�60, write out each sum.
${鈭�}_{k = 0}^{n - 1} \frac{1}{3^{k + 1}}$