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Is there a way to enter this problem in WolframAlpha?:

the sum of the reciprocals of two consecutive integers is -9/20. Find the two integers.

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closed as off topic by acl, Artes, rcollyer, Mr.Wizard Mar 10 '13 at 2:19

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this site is for questions on Mathematica, not Wolfram Alpha (also why the linear-algebra tag?) –  acl Mar 10 '13 at 0:56
To enter a W|A query in Mathematica write == and then solve 1/k+1/(k+1)==-9/20 will return k = -5 as the only integer solution. –  Artes Mar 10 '13 at 0:59
@Artes It's probably worth explicitly pointing out that entering solve 1/k+1/(k+1)==-9/20 directly at the wolfram alpha website returns the answer you mentioned. –  acl Mar 10 '13 at 1:19
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2 Answers

up vote 2 down vote accepted

Just type in the equation portion of acl's answer and you'll see the result n=-5. Here's how it looks in Mathematica:

enter image description here

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Thanks, this worked! –  Jack Stewart Mar 10 '13 at 2:15
@JackStewart Awesome! I would love to point you to a site where WolframAlpha questions are welcomed by knowledgable users. Such questions are certainly not off topic here - just not in vogue. –  Mark McClure Mar 10 '13 at 2:28
@Mark Not trying to pick a fight, but "Such questions are certainly not off topic here"--actually they are; see the faq, where under "Some kinds of questions are considered off-topic" it says "Questions on Wolfram Alpha (but questions on using Wolfram Alpha within Mathematica are okay)". This was a result of discussions, amongst which, this. I know you disagreed, of course. –  acl Mar 10 '13 at 3:13
@MarkMcClure I disagree. Just because W|A is built on Mathematica and a product of the same company, it doesn't mean Mathematica users ought to know more about it than the average person. As I see it, that's rather like posting a message to comp.lang.c++ asking about how to set the page margins in Microsoft Word. After all, Word is written in C++, right? A particular problem with W|A is that nobody really has any idea what input is needed to provoke it into giving a particular result since the parsing is totally opaque and often seemingly arbitrary. –  Oleksandr R. Mar 10 '13 at 3:16
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While questions on Wolfram Alpha are off-topic, here is how to do it in Mathematica:

Reduce[1/n + 1/(n + 1) == -9/20, n, Integers]
(*n == -5*)
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