Q. 12.21 Write the sum using summation no... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 12: Q. 12.21 (page 1171)

Write the sum using summation notation: $\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32} .$

Short Answer

Expert verified

The sum of $\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32}$ can be written in the summation notation as ${鈭�}_{n = 1}^{5} \frac{1}{2^{n}} .$

Step by step solution

Step 1. Given information

$\begin{array}{l} Thegivensumis \\ \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32} \\ Wehavetowritethesumusingsummationnotation. \end{array}$

Step 2. Find the pattern

Now,

We look for a pattern in the terms.

$\begin{matrix} n : & 1 & 2 & 3 & 4 & 5 & ... & n \\ Terms & \frac{1}{2} & \frac{1}{4} & \frac{1}{8} & \frac{1}{16} & \frac{1}{32} & ... \\ Pattern & \frac{1}{2} & \frac{1}{2^{2}} & \frac{1}{2^{3}} & \frac{1}{2^{4}} & \frac{1}{2^{5}} & ... & \frac{1}{2^{n}} \end{matrix}$

Step 3. Conclusion

From the above table, we can observe that all the numerators are 1 and the denominators are 2 raised to the term.

Therefore,

We can write the sum for the 5 terms in summation notation as

${鈭�}_{n = 1}^{5} \frac{1}{2^{n}} .$

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91影视

Write the sum using summation notation: $\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32} .$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the pattern

Step 3. Conclusion

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91影视

Write the sum using summation notation:12+14+18+116+132.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the pattern

Step 3. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

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Study anywhere. Anytime. Across all devices.

Write the sum using summation notation: $\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32} .$