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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 12: Q. 5 (page 839)

Write the following sum using summation notation.
$\frac{- 2}{5} + \frac{3}{6} - \frac{4}{7} + . . . + \frac{11}{14}$

Short Answer

Expert verified

Summation notation of the given sum is ${鈭�}_{k = 1}^{10} [{(- 1)}^{k} (\frac{k + 1}{k + 4})]$ .

Step by step solution

01

Given information:

Consider the given sum, $\frac{- 2}{5} + \frac{3}{6} - \frac{4}{7} + . . . + \frac{11}{14}$

02

Expanding the sum:

$\frac{- 2}{5} + \frac{3}{6} - \frac{4}{7} + \frac{5}{8} - \frac{6}{9} + \frac{7}{10} - \frac{8}{11} + \frac{9}{12} - \frac{10}{13} + \frac{11}{14}$

Here, $k = 1 t o 10$

03

Step 3:

(1) Since the signs in the given sum is alternate, ${(- 1)}^{k}$ .

(2) Numerator : $2, 3, 4, . . ., 11$

The above sequence is one increased by the previous, $i e, k + 1$ .

(3) Denominator : $5, 6, 7, . . ., 14$

The above sequence is four increased by the previous, $i e, k + 4 .$

Summing up 3 points, we get,

${鈭�}_{k = 1}^{10} [{(- 1)}^{k} (\frac{k + 1}{k + 4})]$

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Most popular questions from this chapter

In Problems 71-82, find the sum of each sequence.

${鈭� (3}_{k = 1}^{26} k - 7)$

In a(n) ______sequence the ratio of successive terms is a constant.

In Problems 11鈥�16, evaluate each factorial expression.

$\frac{12!}{10!}$

In Problems 51鈥�60, write out each sum.

${鈭�}_{k = 1}^{n} \frac{k^{2}}{2}$

In Problems 37鈥�50, a sequence is defined recursively. Write down the first five terms.

$a_{1} = 5; a_{n} = 2 a_{n - 1}$

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