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 $\sum_{k = 1}^{10} [{(- 1)}^{k} (\frac{k + 1}{k + 4})]$ .

Step by step solution

Given information:

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

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, $k = 1 t o 10$

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,

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

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

Short Answer

Step by step solution

Given information:

Expanding the sum:

Step 3:

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Write the following sum using summation notation.-25+36-47+...+1114

Short Answer

Step by step solution

Given information:

Expanding the sum:

Step 3:

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Most popular questions from this chapter

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