Chapter 14: Q 31. (page 904)

Confirm the entries in Table 6.
[Hint: Review the formula for the sum of an arithmetic sequence.]

Short Answer

Expert verified

The sum for the left endpoint is 0.5, 0.75, 0.9, and 0.99 and the sum for the right endpoint is 1.5, 1.25, 1.1, and 1.01.

Step by step solution

Step 1. Given information.

Consider the given table,

Step 2. Calculate the sum for the left endpoint.

Find the left endpoint sum.

For n=2,

$0 + 0.5 = 0.5$

For n=4,

$0 + 0.125 + 0.25 + 0.375 = 0.75$

For n = 10,

$\begin{array}{rcl} 0 + 0.02 + 0.04 + 0.06 + 0.08 + 0.10 + 0.12 + 0.14 + 0.16 + 0.18 & = & \frac{10}{2} (0.0.18) \\ = & 0.9 \end{array}$

For n=100,

$\begin{array}{rcl} 0 + 0.0002 + 0.0004 + 0.0006 + 0.0008 + \dots + 0.0198 & = & \frac{100}{2} (0 . + 0.0198) \\ = & 0.99 \end{array}$

Step 3. Find the right endpoint sum.

Find the right endpoint sum.

For n=2,

$0.5 + 1 = 1.5$

For n=4,

$0.125 + 0.25 + 0.375 + 0.5 = 1.25$

For n=10,

$\begin{array}{rcl} 0.02 + 0.04 + 0.06 + 0.08 + 0.10 + 0.12 + 0.14 + 0.16 + 0.18 + 0.20 & = & \frac{10}{2} (0.02 + 0.20) \\ = & 1.1 \end{array}$

For n=100,

$\begin{array}{rcl} 0.0002 + 0.0004 + 0.0006 + \dots + 0.02 & = & \frac{100}{2} (0.0002 + 0.02) \\ = & 1.01 \end{array}$

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Confirm the entries in Table 6.
[Hint: Review the formula for the sum of an arithmetic sequence.]

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculate the sum for the left endpoint.

Step 3. Find the right endpoint sum.

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Confirm the entries in Table 6.[Hint: Review the formula for the sum of an arithmetic sequence.]

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculate the sum for the left endpoint.

Step 3. Find the right endpoint sum.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Decision Maths

Theoretical and Mathematical Physics

Probability and Statistics

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Confirm the entries in Table 6.
[Hint: Review the formula for the sum of an arithmetic sequence.]