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Chapter 4: Q. 3 (page 325)

Explain why it would be difficult to write the sum $\frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{8} + \frac{1}{11} + \frac{1}{12} + \frac{1}{13}$ in sigma notation.

Short Answer

Expert verified

It difficult to write the sum in sigma notation. Because we can't find any pattern to write it in sigma notation.

Step by step solution

01

Step 1. Given Information:

Given sum: $\frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{8} + \frac{1}{11} + \frac{1}{12} + \frac{1}{13}$

We want to explain why it would be difficult to write the sum in sigma notation.

02

Step 2. Solution:

We know that the sigma notation is used to write a sum only when the terms of the sum follow a pattern.

But in given sum $\frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{8} + \frac{1}{11} + \frac{1}{12} + \frac{1}{13}$ it would be difficult to write the sum in sigma notation.

Because we can't find any pattern to write it in sigma notation.

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Most popular questions from this chapter

Write each expression in Exercises 41鈥�43 in one sigma notation (with some extra terms added to or subtracted from the sum, as necessary).

$3 {鈭�}_{k = 2}^{25} k^{2} + 2 {鈭� k}_{k = 2}^{24} - {鈭�}_{k = 0}^{25} 1$

Use integration formulas to solve each integral in Exercises 21鈥�62. You may have to use algebra, educated guess- and- check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating. (Hint for Exercise 54: $\tan (x) = \frac{\sin (x)}{\cos (x)}$ ).

$鈭� (\tan (x) + x \sec^{2} (x)) d x .$

Consider the general sigma notation ${鈭�}_{k = m}^{n} a_{k}$ .What do we mean when we say that a_k is a function of k?

Find the sum or quantity without completely expanding or calculating any sums.

Given ${鈭�}_{k = 0}^{25} k = 325$ and ${鈭�}_{k = 3}^{28} {(k - 3)}^{2} = 14, 910$ , find the value of ${鈭�}_{k = 3}^{25} (k^{2} - 5 k + 9)$ .

Use integration formulas to solve each integral in Exercises 21鈥�62. You may have to use algebra, educated guess- and- check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating. (Hint for Exercise 54: $\tan (x) = \frac{\sin (x)}{\cos (x)}$ ).

$鈭� \frac{e^{3 x} - 2 e^{4 x}}{e^{2 x}} d x$ .

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