This image is a visual proof that \(\sum_{k=1}^{n}k\) equals what?

## Answer.

\(\mathop{\rm C}\nolimits\!\left(n+1,2\right)\hbox{ or }\frac{\left(n+1\right)n}{2}\)

It is natural for exercises to have graphics. For example, an exercise might produce a graph of some kind, and ask the reader to extract some information from that graph.

If your WeBWorK server is version 2.16 or later, WeBWorK problems can process

`<latex-image>`

code. Here is an example.`<latex-image>`

graph.
This image is a visual proof that \(\sum_{k=1}^{n}k\) equals what?

\(\mathop{\rm C}\nolimits\!\left(n+1,2\right)\hbox{ or }\frac{\left(n+1\right)n}{2}\)

`<latex-image>`

graph.
These images may depend on the random seed. In this problem, the height and width of the rectangle are randomized.

Find the area of the rectangle.

\(48\ {\rm cm^{2}}\)

`<latex-image>`

graph affected by `<latex-image-preamble>`

.
This sample chapterâ€™s

`<docinfo>`

has a `<latex-image-preamble>`

. This exercise has graph styling that is affected by that.What are the roots of this polynomial?

\(-3, 0, 3\)

This exercise is to test that special characters behave.

The code below has a printed dollar sign, a printed percent sign, a printed at sign, and a percent sign used as a comment marker.

An older mechanism for creating images is supported and demonstrated here.

The graph below is a graph of \(y=f(x)\text{.}\) Use the graph to solve the equation \(f(x)=1\text{.}\)

\(\left\{1\right\}\)

The graph reveals that the solution set to \(f(x)=1\) is \({\left\{1\right\}}\text{.}\)

This exercisegroup has a

`<latex-image>`

image in its introduction. In standalone versions of the exercise, this image should be repeated.Find \(D\) when \(L=4\) and \(W=3\text{.}\)

\(5\)

Find \(D\) when \(L=12\) and \(W=5\text{.}\)

\(13\)

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