Q. 63 In the following exercise, write... [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. 63 (page 1174)

In the following exercise, write each sum using summation notation.
$1 + \frac{1}{8} + \frac{1}{27} + \frac{1}{64} + \frac{1}{125}$

Short Answer

Expert verified

$1 + \frac{1}{8} + \frac{1}{27} + \frac{1}{64} + \frac{1}{125} = {鈭�}_{n = 1}^{5} \frac{1}{n^{3}}$

Step by step solution

Step 1. Given information

$1 + \frac{1}{8} + \frac{1}{27} + \frac{1}{64} + \frac{1}{125}$

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

Step 2. Explanation

$\begin{array}{l} Thesumofthefirstntermsofasequencewhosenthtermisaniswritteninsummationnotationas: \\ {鈭�}_{i = 1}^{n} a_{i} = a_{i} = a_{1} + a_{2} + a_{3} + a_{4} + a_{5} + 鈥� + a_{n} \\ The i istheindexofsummationandthe1tellsuswheretostartandthentellsuswheretoend. \\ Here \\ \begin{matrix} n : & 1 & 2 & 3 & 4 & 5 \\ Terms: & 1 & \frac{1}{8} & \frac{1}{27} & \frac{1}{64} & \frac{1}{125} \\ Pattern: & \frac{1}{1^{3}} & \frac{1}{2^{3}} & \frac{1}{3^{3}} & \frac{1}{4^{3}} & \frac{1}{5^{3}} & ... & \frac{1}{n^{3}} \end{matrix} \end{array}$

Step 3. Conclusion

$\begin{array}{l} Fromtheabovetable,wecanconcludethatthegeneraltermsis \frac{1}{n^{3}} . \\ Therefore, \\ Thesumwritteninsummationnotationis \\ 1 + \frac{1}{8} + \frac{1}{27} + \frac{1}{64} + \frac{1}{125} = {鈭�}_{n = 1}^{5} \frac{1}{n^{3}} \end{array}$

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91影视

In the following exercise, write each sum using summation notation.
$1 + \frac{1}{8} + \frac{1}{27} + \frac{1}{64} + \frac{1}{125}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

Step 3. Conclusion

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91影视

In the following exercise, write each sum using summation notation.1+18+127+164+1125

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

Step 3. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Applied Mathematics

Decision Maths

Mechanics Maths

Theoretical and Mathematical Physics

Statistics

Study anywhere. Anytime. Across all devices.

In the following exercise, write each sum using summation notation.
$1 + \frac{1}{8} + \frac{1}{27} + \frac{1}{64} + \frac{1}{125}$