## Cancel common factors in symbolic product

Suppose I have the following function

``G[n_, k_] := Product[g[n + i]/g[i], {i, 0, k}] ``

where $$n,k$$ are assumed to be natural numbers and $$g$$ is a nonzero symbolic function. I want to simplify the expression `G[n,k+1]/G[n,k]` and cancel all common terms to get `g[n+k+1]/g[k+1]`. However, `Simplify`, `FullSimplify`, `Expand` and `Cancel` all yield the symbolic (not cancelled) product.

## What are common routes from Shadowdale to Waterdeep?

The party I DM has completed their adventures in the Dalelands (Shadowdale and Daggerdale) and wants to travel to Waterdeep. The party is fairly low level, so their travel will be non-magical and not too expensive. The time period is the 1350s DR, the geography is similar to 5e but not to 4e. What are common routes from Shadowdale to Waterdeep? Bonus points for the time various routes take.

## Does the paladin’s Divine Health feature protect against both common and magical diseases?

By 3rd level, a Paladin gains the following ability (PHB, pg. 85):

Divine Health: The divine magic flowing through you makes you immune to disease.

Does this protect against both common AND magical disease?

There is no differentiation between the two. Disease is simply disease in the relevant entries (which I can’t find anymore). A few spells afflict you with disease; sickly common folk may be diseased, and certain magical aura’s on enemies may inflict a diseased state. Since these all count under the ‘Disease’ umbrella, and the Paladin trait simply says a magical energy is making you immune to disease… I assume this is read as “Immune to [all] disease.”

## Which damage types are the most and least common?

(Inspired by this question)

The only mechanical difference (beside price) between Hide and Scale mail is that once you can use the specialization, the one provides resistance against piercing, the other bludgeoning.

So which is more common, monsters with piercing, bludgeoning or slashing damage?

## Are common potions of healing considered magic items?

I just had a session and there was an argument about this. In the DMG page 187-188 it shows potions of healing in the magic item section. In the PHB page 153 it says they are magical. On DNDBeyond it is considered both magical and mundane when you go to add equipment to your character. One player was saying they are always magic items and another was saying that according to dndbeyond it isn’t always a magic item. Which person is correct?

## Longest common sub sequences with a condition

Consider a sequences if called good if it contains at least one pair one adjacent numbers which are equal.A good sub-sequence of a array is a sub sequence of that array which is good and has its length is highest.Now you are given two array $$S$$ and $$T$$ with integers,you need to find sub sequences with is common to both arrays and has maximum length and is a good sub sequence.

This is a pure dynamic programming problem,in which states are $$dp[i][j]$$ is answer for $$S[1:i]$$ and $$T[1:j]$$ ($$A[1:i]$$ means subarray of $$A$$ from $$1$$ to $$i$$). But i could not find transition between states,could anyone help me.

## Is it possible to make a common PC bluetooth card identify itself as headset? [closed]

My objective would be to make an application that makes the computer identify as a headset, so I can connect my phone to it and route the audio of the calls to the computer.

I think this is highly related to security. I’m talking about the ability to make a device identify as something else, think about the USB rubber ducky, now replace "USB" with "Bluetooth".

That’s why I posted here. The purpose of doing this would not be anything malicious, I just want to connect my phone to the PC so I can hear the voice of the person calling me on my phone, through the headset connected to my PC:

Phone -> Bluetooth -> Computer -> Headset

## What deities are common knowledge along the northern parts of the Sword Coast? (post-1480 DR)

Specifically between Neverwinter and Icewind Dale, which religions are common knowledge in the years following 1480 DR?

Common knowledge being that if a player character grew up in this area, they would realistically already know that that deity is a deity and maybe something about their religion.

Example: When asked, the average person in the region may say "Mystra is the deity of Magic" if Mystra and her religion are common knowledge.

## Atheism in the DnD5e universe: is it a thing, and how common is it? Are clerics accepted to derive power from the divine?

My question comes up from a bit of weird exchange we had last session. Short version of the question: Is not believing in the existence of gods in most DnD universes really a widespread thing? Are clerics that can tap into these abilities very uncommon or believed to get their magic from some other source? And if no to these, how does one handle PC’s behaving as if this were so?

Long version: I ended up multiclassing cleric through a pretty cool set of story hooks that my DM did a good job working with me in setting up. I definitely wasn’t a stereotypical stoic priest preaching about my god or anything like that.

In terms of story as it played out when I revealed this new power to the rest of the party (which they were present OOC for me receiving), one of our party had a roleplay situation that came where I could use my new class to help, and I told the rest of party that if they would help me, I’d like to offer this help to the other PC (the object of the help was not present IC so didn’t react).

I was kinda bummed that the reception was anywhere from condescension to incredulity (both IC and OOC), at least one of them heavily implying that thinking a god exists is stupid, and I really felt like this was out of place; my impression (granted, as someone fairly new to this) was that the existence of gods in the DnD universes are no more contested than the existence of magic: it exists, everyone knows it exists whether or not they’ve directly been affected by it. Is this impression wrong? I feel as though nobody would have blinked if I multiclassed into warlock and made a pact with a supernatural being, but for some reason because it was explicitly a ‘god’ I attuned to there was a lot more incredulity.

I’m not really sure how to handle this going forward. Is this the sort of thing I should talk the DM about and get straight? Should I talk with the other players directly? Is my impression on the wide acceptance of gods just wrong? Not sure how to deal with this, IC or OOC. It sorta sucks, because I was really excited for this multiclass and I walked away feeling kinda dumb and not really being into it anymore. Thanks for suggestions.

E: Should have mentioned, we are using homebrew that seems to get material like this from Forgotten Realms based on our warlock’s already-existing pact. DM hasn’t mentioned to either of us to tailor our choices of being to his setting.

## Are all mundane items of common rarity?

Magic items range in rarity from Common to Artifact. However, I can’t find any mundane items that go beyond Common.

Are there any non-magical items of Uncommon rarity or higher? If so, a list/database would be great. If not, is this an intentional design decision? Could a DM create an uncommon mundane item under RAW?