Chapter 12: Q. 255 (page 1217)

In the following exercises, expand the partial sum and find its value.
$\sum_{k = 0}^{4} \frac{4}{k!}$

Short Answer

Expert verified

The partial sum is $\frac{65}{6}$ .

Step by step solution

Step 1. Given information.

The given expression is,

$\sum_{k = 0}^{4} \frac{4}{k!}$ .

Step 2. Finding the partial sum.

Now, to expand the partial sum we will substitute $0, 1, 2, 3,$ and $4$ respectively and then simplify.

$\sum_{k = 0}^{4} \frac{4}{k!} = \frac{4}{0!} + \frac{4}{1!} + \frac{4}{2!} + \frac{4}{3!} + \frac{4}{4!} = \frac{4}{1} + \frac{4}{1} + \frac{4}{2} + \frac{4}{6} + \frac{4}{24} = 4 + 4 + 2 + \frac{4}{6} + \frac{1}{6} = 10 + \frac{5}{6} = \frac{60 + 5}{6} = \frac{65}{6}$

Therefore, the partial sum is $\frac{65}{6}$ .

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In the following exercises, expand the partial sum and find its value.
$\sum_{k = 0}^{4} \frac{4}{k!}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Finding the partial sum.

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In the following exercises, expand the partial sum and find its value.∑k=044k!

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Finding the partial sum.

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

In the following exercises, expand the partial sum and find its value.
$\sum_{k = 0}^{4} \frac{4}{k!}$