Chapter 12: Q 59. (page 809)

In Problems 51–60, write out each sum.
$\sum_{k = 2}^{n} {(- 1)}^{k} In k$

Short Answer

Expert verified

The required sum is $\sum_{k = 2}^{n} {(- 1)}^{k} In k = \{In 2 - In 3 + In 4 - . . . . . . . + {(- 1)}^{n} In n\}$ .

Step by step solution

Step 1. Write the given information.

The given summation notation is:

$\sum_{k = 2}^{n} {(- 1)}^{k} In k$

Step 2. Write out the sum.

To get the sum, we need to substitute

2, 3, 4, . . . . ., n

for k,in the given sequence

\sum_{k = 2}^{n} {(- 1)}^{k} In k

$\sum_{k = 2}^{n} {(- 1)}^{k} In k = \{{(- 1)}^{2} In 2 + {(- 1)}^{3} In 3 + {(- 1)}^{4} In 4 + . . . . . . . + {(- 1)}^{n} In n\} = \{In 2 - In 3 + In 4 - . . . . . . . + {(- 1)}^{n} In n\}$

Therefore, $\sum_{k = 2}^{n} {(- 1)}^{k} In k = \{In 2 - In 3 + In 4 - . . . . . . . + {(- 1)}^{n} In n\}$ .

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In Problems 51–60, write out each sum.
$\sum_{k = 2}^{n} {(- 1)}^{k} In k$

Short Answer

Step by step solution

Step 1. Write the given information.

Step 2. Write out the sum.

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In Problems 51–60, write out each sum.∑k=2n-1kInk

Short Answer

Step by step solution

Step 1. Write the given information.

Step 2. Write out the sum.

One App. One Place for Learning.

Most popular questions from this chapter

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In Problems 51–60, write out each sum.
$\sum_{k = 2}^{n} {(- 1)}^{k} In k$