ARQMath Answer Retrieval for Questions on Math

https://www.cs.rit.edu/~dprl/ARQMath

Richard Zanibbi, Anurag Agarwal, Behrooz Mansouri, and Wei Zhong Douglas W. Oard

rxzvcs@rit.edu, axasma@rit.edu, bm3302@rit.edu, wxz8033@rit.edu oard@umd.edu

Rochester Institute of Technology, USA University of Maryland, USA

#ARQMath

— Goals — Advance math-aware search

Advance semantic analysis of mathematical notation and text

— Collection — Archived posts from Math Stack Exchange (community QA forum)

(~1 million questions; ~28 million LaTeX formulas)Stored in linked XML files

Tools to parse data into question threads provided (python)HTML for threads provided (for study, checking, and evaluation)

Separate Formula Indices (TSV files):appearance encodings: LaTeX, Presentation MathML

semantic encoding: Content MathMLARQMath

2

Task 1: Find Answers to Math Questions (98 Topics)

Mathematics Stack Exchange is a questionand answer site for people studying math atany level and professionals in related fields. Itonly takes a minute to sign up.

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Anybody can ask a question

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The best answers are voted up andrise to the top

How can I evaluate ?(! + 1)!"!=0 "!

Asked 8 years, 5 months ago Active 4 months ago 34k timesViewed

384

146

How can I evaluate

I know the answer thanks to , but I'm more concerned with how I can derivethat answer. It cites tests to prove that it is convergent, but my class has never learned thesebefore so I feel that there must be a simpler method.

!!=1

" 2!3!+1

Wolfram Alpha

In general, how can I evaluate

(! + 1) ?!!=0

""!

sequences-and-series convergence power-series faq

edited Sep 24 '17 at 12:09

Parcly Taxel51.7k 13 80 120

asked Apr 3 '11 at 21:41

Backus2,072 3 12 8

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Query Search Results

How can I evaluate ?(! + 1)!"!=0 "!

Asked 8 years, 5 months ago Active 4 months ago 34k timesViewed

384

146

How can I evaluate

I know the answer thanks to , but I'm more concerned with how I can derivethat answer. It cites tests to prove that it is convergent, but my class has never learned thesebefore so I feel that there must be a simpler method.

!!=1

" 2!3!+1

Wolfram Alpha

In general, how can I evaluate

(! + 1) ?!!=0

""!

sequences-and-series convergence power-series faq

edited Sep 24 '17 at 12:09

Parcly Taxel51.7k 13 80 120

asked Apr 3 '11 at 21:41

Backus2,072 3 12 8

2–

I believe this is an arithmo-geometric series. You can find information here:artofproblemsolving.com/wiki/… Jason Kim Jul 7 '18 at 19:11

19 Answers

338

+150

No need to use Taylor series, this can be derived in a similar way to the formula forgeometric series. Let's find a general formula for the following sum:

= ! .#$ !!=1

$%!

Notice that

# %#$ #$ = #$ +%$+1 !$

%!

…

…

…

.

.

.

1

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3

Given a posted question (in 2019) as a query: search answer posts (2010-2018)

return relevant answers

3ARQMath

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1

2

3

Mathematics Stack Exchange is a questionand answer site for people studying math atany level and professionals in related fields. Itonly takes a minute to sign up.

Sign up to join this community

Anybody can ask a question

Anybody can answer

The best answers are voted up andrise to the top

How can I evaluate ?(! + 1)!"!=0 "!

Asked 8 years, 5 months ago Active 4 months ago 34k timesViewed

384

146

How can I evaluate

I know the answer thanks to , but I'm more concerned with how I can derivethat answer. It cites tests to prove that it is convergent, but my class has never learned thesebefore so I feel that there must be a simpler method.

!!=1

" 2!3!+1

Wolfram Alpha

In general, how can I evaluate

(! + 1) ?!!=0

""!

sequences-and-series convergence power-series faq

edited Sep 24 '17 at 12:09

Parcly Taxel51.7k 13 80 120

asked Apr 3 '11 at 21:41

Backus2,072 3 12 8

By using our site, you acknowledge that you have read and understand our , ,

and our .

Cookie Policy Privacy Policy

Terms of Service

Mathematics Stack Exchange is a questionand answer site for people studying math atany level and professionals in related fields. Itonly takes a minute to sign up.

Sign up to join this community

Anybody can ask a question

Anybody can answer

The best answers are voted up andrise to the top

How can I evaluate ?(! + 1)!"!=0 "!

Asked 8 years, 5 months ago Active 4 months ago 34k timesViewed

384

146

How can I evaluate

I know the answer thanks to , but I'm more concerned with how I can derivethat answer. It cites tests to prove that it is convergent, but my class has never learned thesebefore so I feel that there must be a simpler method.

!!=1

" 2!3!+1

Wolfram Alpha

In general, how can I evaluate

(! + 1) ?!!=0

""!

sequences-and-series convergence power-series faq

edited Sep 24 '17 at 12:09

Parcly Taxel51.7k 13 80 120

asked Apr 3 '11 at 21:41

Backus2,072 3 12 8

By using our site, you acknowledge that you have read and understand our , ,

and our .

Cookie Policy Privacy Policy

Terms of Service

Mathematics Stack Exchange is a questionand answer site for people studying math atany level and professionals in related fields. Itonly takes a minute to sign up.

Sign up to join this community

Anybody can ask a question

Anybody can answer

The best answers are voted up andrise to the top

Evaluate the integral: d!! 10

ln(!+1)+1!2

Asked 7 years, 3 months ago Active 2 years, 7 months ago 20k timesViewed

87

53

Compute

d!!1

0

ln(! + 1)+ 1!2

calculus real-analysis integration definite-integrals

edited Aug 29 '14 at 22:39

Ali Caglayan3,793 8 32 64

asked Jun 9 '12 at 7:49

user 135711323k 9 80 230

– wolfram gives the answer as 0.272198 user9413 Jun 9 '12 at 7:57

– Mathematica gives the answer . But I do not know how it computed this number...log 2"8 Siminore

Jun 9 '12 at 8:25

– @Chris: Even, i thought of that only :) user9413 Jun 9 '12 at 8:26

7

–

Why dont you try and solve these Integrals yourself. Browsing through your most recent questions,you have had this type of question almost exclusively. Other users get downvoted for this. I see noreason not to hint the same to you and at least show some effort. -1 CBenni Mar 20 '13 at 17:01

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and our .

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Task 2: Formula Search (in-context)(87 Topics)

Given formula in a question post from Task 1 (2019): search formulas in question and answer posts (2010-2018)

return relevant formulas w. associated posts Mathematics Stack Exchange is a questionand answer site for people studying math atany level and professionals in related fields. Itonly takes a minute to sign up.

Sign up to join this community

Anybody can ask a question

Anybody can answer

The best answers are voted up andrise to the top

How can I evaluate ?(! + 1)!"!=0 "!

Asked 8 years, 5 months ago Active 4 months ago 34k timesViewed

384

146

How can I evaluate

I know the answer thanks to , but I'm more concerned with how I can derivethat answer. It cites tests to prove that it is convergent, but my class has never learned thesebefore so I feel that there must be a simpler method.

!!=1

" 2!3!+1

Wolfram Alpha

In general, how can I evaluate

(! + 1) ?!!=0

""!

sequences-and-series convergence power-series faq

edited Sep 24 '17 at 12:09

Parcly Taxel51.7k 13 80 120

asked Apr 3 '11 at 21:41

Backus2,072 3 12 8

By using our site, you acknowledge that you have read and understand our , ,

and our .

Cookie Policy Privacy Policy

Terms of Service

4ARQMath

Mathematics Stack Exchange is a questionand answer site for people studying math atany level and professionals in related fields. Itonly takes a minute to sign up.

Sign up to join this community

Anybody can ask a question

Anybody can answer

The best answers are voted up andrise to the top

How can I evaluate ?(! + 1)!"!=0 "!

Asked 8 years, 5 months ago Active 4 months ago 34k timesViewed

384

146

How can I evaluate

I know the answer thanks to , but I'm more concerned with how I can derivethat answer. It cites tests to prove that it is convergent, but my class has never learned thesebefore so I feel that there must be a simpler method.

!!=1

" 2!3!+1

Wolfram Alpha

In general, how can I evaluate

(! + 1) ?!!=0

""!

sequences-and-series convergence power-series faq

edited Sep 24 '17 at 12:09

Parcly Taxel51.7k 13 80 120

asked Apr 3 '11 at 21:41

Backus2,072 3 12 8

By using our site, you acknowledge that you have read and understand our , ,

and our .

Cookie Policy Privacy Policy

Terms of Service

1

2

3

1

2

3

Query Search Results

Evaluation for Task 2: Formula Search (in-context)

5

Per topic: Unique formulas pooled by appearance; posts sampled from threadsFormulas in sampled posts evaluated separately (i.e., in-context)

Runs for both tasks ranked via nDCG (nDCG using only evaluated hits)′

Evaluation tools built with Turkle: https://github.com/hltcoe/turkle

Sakai, T. & Kando, N. (2008). On information retrieval metrics designed for evaluation with incomplete relevance assessments. Information Retrieval.

Multi-level relevance

— Baseline Systems — Our baseline systems are open-source

Each will be configured to index the ARQMath collection

Task 1: Approach0 (Zhong et al., https://approach0.xyz/search)Ad-hoc math-aware search engine (text + math)

formulas: semantic encoding

Task 2: Tangent-s (Davila et al., https://www.cs.rit.edu/~dprl/software.html)Formula search engine (math only)

formulas: appearance + semantic encodings

ARQMath6

Kenny Davila, Richard Zanibbi: Layout and Semantics: Combining Representations for Mathematical Formula Search. SIGIR 2017: 1165-1168

Wei Zhong, Hui Fang: OPMES: A Similarity Search Engine for Mathematical Content. ECIR 2016: 849-852

ARQMath Answer Retrieval for Questions on Math

https://www.cs.rit.edu/~dprl/ARQMath

#ARQMath

Please join us! Send Email to: rxzvcs@rit.edu

Thanks to the National Science Foundation (USA) for their support