Q. 61 In the following exercises, writ... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 12: Q. 61 (page 1174)

In the following exercises, write each sum using summation notation.
$\frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \frac{1}{81} + \frac{1}{243}$

Short Answer

Expert verified

$\begin{array}{l} Thesumwritteninsummationnotationis \\ \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \frac{1}{81} + \frac{1}{243} = {鈭�}_{n = 1}^{5} \frac{1}{3^{n}} \end{array}$

Step by step solution

Step 1. Given informaiton

$\frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \frac{1}{81} + \frac{1}{243}$

In the following exercises, write each sum using summation notation.

Step 2. Explanation

$\begin{array}{l} Thesumofthefirstntermsofasequencewhosenthtermisaniswritteninsummationnotationas: \\ {鈭�}_{i = 1}^{n} a_{i} = a_{i} = a_{1} + a_{2} + a_{3} + a_{4} + a_{5} + 鈥� + a_{n} \\ The i istheindexofsummationandthe1tellsuswheretostartandthentellsuswheretoend. \\ Here \\ \begin{matrix} n : & 1 & 2 & 3 & 4 & 5 \\ Terms: & \frac{1}{3} & \frac{1}{9} & \frac{1}{27} & \frac{1}{81} & \frac{1}{243} \\ Pattern: & \frac{1}{3^{1}} & \frac{1}{3^{2}} & \frac{1}{3^{3}} & \frac{1}{3^{4}} & \frac{1}{3^{5}} & ... & \frac{1}{3^{n}} \end{matrix} \end{array}$

Step 3. Conclusion

$\begin{array}{l} Fromtheabovetable,wecanconcludethatthegeneraltermsis \frac{1}{3^{n}} . \\ Therefore, \\ Thesumwritteninsummationnotationis \\ \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \frac{1}{81} + \frac{1}{243} = {鈭�}_{n = 1}^{5} \frac{1}{3^{n}} \end{array}$

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91影视

In the following exercises, write each sum using summation notation.
$\frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \frac{1}{81} + \frac{1}{243}$

Short Answer

Step by step solution

Step 1. Given informaiton

Step 2. Explanation

Step 3. Conclusion

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91影视

In the following exercises, write each sum using summation notation.13+19+127+181+1243

Short Answer

Step by step solution

Step 1. Given informaiton

Step 2. Explanation

Step 3. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Calculus

Theoretical and Mathematical Physics

Geometry

Discrete Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, write each sum using summation notation.
$\frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \frac{1}{81} + \frac{1}{243}$