Q. 30 Write out each sum in Exercises ... [FREE SOLUTION]

Chapter 4: Q. 30 (page 325)

Write out each sum in Exercises 30 in expanded form, and then calculate the value of the sum.
${鈭�}_{k = 0}^{6} \frac{2}{k + 1}$

Short Answer

Expert verified

The expanded notation is $\begin{array}{rcl} 2 + \frac{2}{2} + \frac{2}{3} + \frac{2}{4} + \frac{2}{5} + \frac{2}{6} + \frac{2}{7} \end{array}$ and their sum is $\frac{3267}{630}$ or $5.186$ .

Step by step solution

Given information

The given summation is ${鈭�}_{k = 0}^{6} \frac{2}{k + 1}$ .

Write the summation in expanded form and evaluate the sum.

Rewrite the given summation in expanded form.

$\begin{array}{rcl} {鈭�}_{k = 0}^{6} \frac{2}{k + 1} & = & \frac{2}{0 + 1} + \frac{2}{1 + 1} + \frac{2}{2 + 1} + \frac{2}{3 + 1} + \frac{2}{4 + 1} + \frac{2}{5 + 1} + \frac{2}{6 + 1} \\ = & 2 + \frac{2}{2} + \frac{2}{3} + \frac{2}{4} + \frac{2}{5} + \frac{2}{6} + \frac{2}{7} \\ = & 2 + 1 + \frac{2}{3} + \frac{1}{2} + \frac{2}{5} + \frac{1}{3} + \frac{2}{7} \\ = & 3 + \frac{4 + 3}{6} + \frac{6 + 5}{15} + \frac{2}{7} \\ = & 3 + \frac{7}{6} + \frac{11}{15} + \frac{2}{7} \\ = & \frac{1890 + 735 + 462 + 180}{630} \\ = & \frac{3267}{630} \\ = & 5.186 \end{array}$

Write the conclusion

The expanded form is $\begin{array}{rcl} 2 + \frac{2}{2} + \frac{2}{3} + \frac{2}{4} + \frac{2}{5} + \frac{2}{6} + \frac{2}{7} \end{array}$ and their sum is $\frac{3267}{630}$ or $5.186$ .

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Write out each sum in Exercises 30 in expanded form, and then calculate the value of the sum.
${鈭�}_{k = 0}^{6} \frac{2}{k + 1}$

Short Answer

Step by step solution

Given information

Write the summation in expanded form and evaluate the sum.

Write the conclusion

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91影视

Write out each sum in Exercises 30 in expanded form, and then calculate the value of the sum.鈭�k=062k+1

Short Answer

Step by step solution

Given information

Write the summation in expanded form and evaluate the sum.

Write the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

Write out each sum in Exercises 30 in expanded form, and then calculate the value of the sum.
${鈭�}_{k = 0}^{6} \frac{2}{k + 1}$