Wikipedia:Reference desk/Archives/Mathematics/2024 February 10
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February 10
editSum n =1->Inf of 1/(n^p)
editI know that this sum is infinite if p is 1 and finite if p = 2, but where is the crossing line. Is it finite or infinite for 1.1? 1.5? 1.9? Naraht (talk) 02:35, 10 February 2024 (UTC)
- It's finite for all p > 1, and infinite at p = 1. Wikipedia:Reference desk/Archives/Mathematics/2023 November 1#Border between finite and infinite has some more useful information. GalacticShoe (talk) 02:47, 10 February 2024 (UTC)
- Thank you!Naraht (talk) 03:08, 10 February 2024 (UTC)
- @Naraht: You should also know that this function has a name. It's called the Riemann zeta function. More precisely, , where is the function in question. Duckmather (talk) 02:40, 13 February 2024 (UTC)
- The more common use of the colon equals symbol in a definition is to put the definiendum on the lhs and the definiens on the rhs:[1]
- Since the symbol is asymmetric, one might use an equals colon for the reverse defining direction:
- However, while readily understandable, this is not common usage. --Lambiam 10:07, 13 February 2024 (UTC)
- The more common use of the colon equals symbol in a definition is to put the definiendum on the lhs and the definiens on the rhs:[1]