delete 1, 2, 3, 4

delete 5, 6, 7, 8

delete 9, 10, 11, 12

duplicate This has been asked and answered before, there are (at least) 3 possible duplicate targets.

OTOH regarding the context provided by the OP, the today's post 3081320: Is it true that $\forall n \in \Bbb{N} : (\sum_{i=1}^{n} a_{i} ) (\sum_{i=1}^{n} \frac{1}{a_{i}} ) \ge n^2$ , if all $a_{i}$ are positive? seems to be better of than the older posts.

So it's at least worth considering whether the newer post should not be a duplicate target. (Although it's clear that some regulars of this room will tell me that they prefer other forms of context than an OP's attempt. And 504240 Proof that $\left(\sum^n_{k=1}x_k\right)\left(\sum^n_{k=1}y_k\right)\geq n^2$ provides at least some context.)

Btw, I wonder why the name “Schwarz” is so often misspelled as “Schwartz” – there are 495 search results for “Cauchy-Schwartz”

... compared to 5,267 results for the correct “Cauchy-Schwarz”.

440761: Induction of inequality involving AP seems to be about the same problem (or at least the first part) - it asks specifically for proof by induction.

One more duplicate - 2134362: How do I prove this using question using Cauchy-Schwarz inequality?.

And perhaps a few other result from this search: approach0.xyz/search/…

duplicates So these are (at least some) questions about the same inequality: 504240, 912314, 1162430, 1506405, 1871864, 2134362, 3081320.

1506405 specifically asks for prove using induction. 2134362 specifically asks for a proof using Cauchy-Schwarz inequality.

Which of them should be left open? Which is the most suitable as a duplicate target?

@Lord_Farin (9) doesn't seem too bad, but the rest are gone except 10.

@XanderHenderson Up for deletion now.

^ Look at that, 2 reopen-votes already!

Delete? A, B, C.

D, E, F.

G, H, I.

J, K, L.

@user21820 I don't know. "Prove this arbitrary identity, which happens to be false." True, there was some effort shown, but I wouldn't contend it to have lasting value.

@Lord_Farin Sure; I agree it has no lasting value.

And indeed that's a fault of the SE system; once people post an answer the asker cannot delete the question, and the 'right' way would be to post a comment saying it's wrong and that's all there is to it.

@MartinSleziak I haven't checked all of them, but it seems to me that 504240 is a good target – it covers all approaches (AM/HM, C-S, induction, x+1/x >=2).

@MartinR That sounds reasonable - at least from the viewpoint of quality of the answers posted there.

Perhaps we should add some tags – at least [inequality].

Perhaps it could serve as a duplicate target for now - and if it is closed for lack of context, we can search for a better one. (Although the question has at least some explanation by the OP about unsuccessful application of Cauchy-Schwarz.)

I saw that one of the posts had an answer with rearrangement inequality.

Here is a solution using rearrangement inequality. And convexity of 1/x seems interesting too - although it is basically just HM-AM

merging Are the answers on 1871864: Prove inequality $(a_1+a_2+...+a_n)(\frac1{a_1}+\frac1{a_2}+...+\frac1{a_n})\geq n^2$ when $a_1,a_2,...,a_n$ are positive numbers. mentioned above (convexity, rearrangement) interesting enough for them to be merged into the duplicate target?

@MartinSleziak Sounds good to me: Merge 1871864 into 504240, and close the others as a duplicate of the latter.

@MartinR I have added some tags - inequality, summation, cauchy-schwarz-inequality. If some of them are redundant, feel free to retag the post.

Ok, I'd suggest to wait until the questions are closed. (And also to see whether there are some objections.) After that, somebody can flag for merging.

Merging might require editing one of them (probably the one that is closed) - since the variables are a_1,...,a_n vs. x_1,...,x_n; so the answers would have different notation from the question. But if the questions are merged, I am certainly willing to do the editing.

special snowflake needs step by step instructions to pass weird PHD qual system math.stackexchange.com/questions/3082073/…

@rschwieb Closed.

halleluja

close Duplicate, but should just be removed.

Meh, 2-questions-in-one review audit failed.

close delete Finding remainders, Finding more remainders. Hours apart :(

I suggested a duplicate here math.stackexchange.com/q/2654173/29335

For deletion: D1, D2, D3, D4, D5, D6, D7

For deletion: D8, D9, D10, D11, D12, D13, D14

For deletion: D15, D16, D17, D18

ugh. Delete this? math.stackexchange.com/q/427803/29335

@rschwieb: I would say so.

yeah, it was more of a rhetorical question. We need a new punctuation for that.

another dupe math.stackexchange.com/q/3082366/29335

Is this chatroom for dealing with questions like this one? I can't vote to close (only flag for closure), and I can downvote. Given the room's description, perhaps some here want to look at the linked question. Thanks!

@jordan_glen If you believe that a question should be closed and that it isn't being handled appropriately on the main site, then this is a good place to mention it.

@rschwieb Agreed. It is gone now.