Chapter 12: Q. 69 (page 1175)

In the following exercise, write each sum using summation notation.
$- 2 + 4 - 6 + 8 - 10 + \dots + 20$

Short Answer

Expert verified

$- 2 + 4 - 6 + 8 - 10 + \dots + 20 = \sum_{n = 1}^{10} {(- 1)}^{n} 2 n$

Step by step solution

Step 1. Given information

$- 2 + 4 - 6 + 8 - 10 + \dots + 20$

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

Step 2. Explanation

$\begin{array}{l} Thesumofthefirstntermsofasequencewhosenthtermisaniswritteninsummationnotationas: \\ \sum_{i = 1}^{n} a_{i} = a_{1} + a_{2} + a_{3} + a_{4} + a_{5} +…+ a_{n} \\ Theiistheindexofsummationandthe1tellsuswheretostartandthentellsuswheretoend. \\ H e r e, \\ \begin{matrix} n & 1 & 2 & 3 & 4 & 5 & ... & 10 \\ Terms: & - 2 & 4 & - 6 & 8 & - 10 & 20 \\ Pattern: & {(- 1)}^{1} 2 (1) & {(- 1)}^{2} 2 (2) & {(- 1)}^{3} 2 (3) & {(- 1)}^{4} 2 (4) & {(- 1)}^{5} 2 (5) & {(- 1)}^{10} 2 (10) & ... & {(- 1)}^{n} 2n \end{matrix} \end{array}$

Step 3. Conclusion

$\begin{array}{l} Fromtheabove,wecanconcludethatthegeneraltermsis2n \\ Therefore, \\ Thesumwritteninsummationnotationis \\ - 2 + 4 - 6 + 8 - 10 + \dots + 20 = \sum_{n = 1}^{10} {(- 1)}^{n} 2 n \end{array}$

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In the following exercise, write each sum using summation notation.
$- 2 + 4 - 6 + 8 - 10 + \dots + 20$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

Step 3. Conclusion

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In the following exercise, write each sum using summation notation.−2+4−6+8−10+…+20

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

Logic and Functions

Statistics

Mechanics Maths

Calculus

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercise, write each sum using summation notation.
$- 2 + 4 - 6 + 8 - 10 + \dots + 20$