Runestone multiple correct MC issue

Mitch Keller

unread,

Jul 9, 2026, 5:23:02 PMJul 9

to 'Rob Beezer' via PreTeXt support

One of our grad students coded up Worksheet Exercise 11.2.2, and we’re seeing some weird behavior. The correct answers are A, D, E, F, G, H, I, and K. If you select all of those and click Check Me, it says “You gave 8 answers and got 2 correct of 8 needed.” If you check all the correct answers except K, it says “You gave 7 answers and got 7 correct of 8 needed.” If you select K and A and five of the other six correct answers, you get "You gave 7 answers and got 2 correct of 8 needed.” If you select all the correct answers except A, the report is "You gave 7 answers and got 1 correct of 8 needed.” The code lives on our Gitlab and is in a private repository, but I’ve pasted the code for this particular exercise at the end of the message.

Any thoughts on what is wrong here?

Thanks,

Mitch

--
Mitch Keller
mi...@rellek.net

http://www.rellek.net/

Let

<m>

\ds{\sum_{n=1}^{\infty} a_n}

</m>

be a series, and let

<m>

S_{n}

</m>

be the

<m>

n

</m>

th partial sum of the series. Someone hands you a formula for

<m>

S_{n}

</m>

, given by

<m>

\ds{S_n=\frac{4}{1+\frac{1}{n}}}

</m>

for all

<m>

n \geq 1

</m>

. Based on this information, which of the following statements

<alert>

must

</alert>

be true? Circle all correct answers and explain your reasoning.

</statement>

The sequence

<m>

\{S_{n}\}

</m>

converges to

<m>

4

</m>

</statement>

True because

<m>

\ds \lim_{n\to\infty}\frac{4}{1+\frac{1}{n}}=4.

</m>

</feedback>

</choice>

The sequence

<m>

\{S_{n}\}

</m>

diverges

</statement>

False.

</feedback>

</choice>

<m>

\ds{\sum_{n=1}^{\infty} a_n}

</m>

diverges

</statement>

False.

</feedback>

</choice>

<m>

\ds{\sum_{n=1}^{\infty} a_n}

</m>

converges

</statement>

True because once we know that (a) is true, we know that the sequence of partial sums converges. This is the definition of what it means for a series to converge.

</feedback>

</choice>

<m>

\ds{\sum_{n=1}^{\infty} a_n=4}

</m>

</statement>

True because the sequence of partial sums converges to 4. This is the definition of what it means for the series to converge to 4.

</feedback>

</choice>

<m>

\ds{\sum_{n=1}^{\infty} 5a_n=20}

</m>

</statement>

True:

<md>

\sum_{n=1}^{\infty} 5a_{n} = 5\sum_{n=1}^{\infty} a_{n} = 5\cdot 4=20.

</md>

</feedback>

</choice>

<m>

\ds{a_5 = \frac{4}{1+\frac{1}{5}}-\frac{4}{1+\frac{1}{4}}}

</m>

</statement>

True. You can see this by computing terms, but a faster way is to use problem 1. Notice that

<m>

\frac{4}{1+\frac{1}{5}}=S_{5}

</m>

and

<m>

\frac{4}{1+\frac{1}{4}}=S_{4}.

</m>

By problem 1 we know that

<m>

a_{5}=S_{5}-S_{4}

</m>

, so this must be true.

</feedback>

</choice>

<m>

\ds{a_n=\frac{4}{1+\frac{1}{n}}-\frac{4}{1+\frac{1}{n-1}}}

</m>

for

<m>

n \geq 2

</m>

</statement>

True. We again get this for free by number 1. We have that

<m>

S_{n}=\frac{4}{1+\frac{1}{n}}

</m>

and

<m>

S_{n-1}=\frac{4}{1+\frac{1}{n-1}},

</m>

so in other words this question is asking if

<m>

a_{n}=S_{n}-S_{n-1},

</m>

but in number one we showed that this is always true.

</feedback>

</choice>

The sequence

<m>

\{a_{n}\}

</m>

converges

</statement>

True. We've already justified that the series converges; in order for this to be true, the sequence

<m>

\{a_{n}\}

</m>

must converge.

</feedback>

</choice>

The sequence

<m>

\{a_{n}\}

</m>

converges to 4

</statement>

False, the sequence

<m>

a_{n}

</m>

converges to 0.

</feedback>

</choice>

<m>

\ds{\lim_{n\to\infty} a_n=0}

</m>

</statement>

True. We've already justified that the series converges; in order for this to be true, the sequence

<m>

\{a_{n}\}

</m>

must converge. In particular the sequence must converge to 0. (Think about the divergence test, if the sequence

<m>

\{a_{n}\}

</m>

did not converge to 0, then we'd immediately get that the series diverges.

</feedback>

</choice>

</choices>

</exercise>

Andrew Scholer

unread,

Jul 9, 2026, 8:33:35 PMJul 9

to pretext...@googlegroups.com

Looks like you have discovered a bug that has existed for many years but will only affect problems with 10+ answers. (The code sorts 10 between 1 and 2.) I guess no one else has pushed multiple choice / multiple answer problems that far.

I'll send Brad a PR for RS.

--
You received this message because you are subscribed to the Google Groups "PreTeXt support" group.
To unsubscribe from this group and stop receiving emails from it, send an email to pretext-suppo...@googlegroups.com.
To view this discussion visit https://groups.google.com/d/msgid/pretext-support/55A2DDBD-6CE5-494A-8B85-3661CCF7A5D0%40rellek.net.

Mitch Keller

unread,

Jul 10, 2026, 9:33:27 AMJul 10

to pretext...@googlegroups.com

Thanks, Andrew!

To view this discussion visit https://groups.google.com/d/msgid/pretext-support/CACm44N-QgZR%3D0YNmNH1hkc5vX_GqODy6W3Js8Ti%3Dp8pnPGVpiQ%40mail.gmail.com.

Bradley Miller

unread,

Jul 10, 2026, 9:45:34 PMJul 10

to PreTeXt support

I've done a release with Andrew's fix so a rebuild should work for you.

Rob Beezer

unread,

Jul 11, 2026, 3:22:29 PMJul 11

to pretext...@googlegroups.com

On 7/9/26 17:32, Andrew Scholer wrote:
> Looks like you have discovered a bug that has existed for many years but will
> only affect problems with 10+ answers.

"Given enough eyeballs, all bugs are shallow."

Linus's Law, coined by Eric S. Raymond, The Cathedral and the Bazaar (1999).

Mitch Keller

unread,

Jul 13, 2026, 1:56:01 PMJul 13

to pretext...@googlegroups.com

Confirmed working. Many thanks!

To view this discussion visit https://groups.google.com/d/msgid/pretext-support/6586c3e0-7094-4793-8004-8a45d51a9359n%40googlegroups.com.

Reply all

Reply to author

Forward