A Most Unfair Test Question: Combining Sequence Notation and Log Notation in the Same Problem

If you ever wanted to know how to trigger a mathematician, this would be the way to do it. This is the worst misuse of mathematical notation I've ever seen. It combines sequence notation (subscripts that don't typically have operational value) with logarithmic base notation (subscripts that DO have operational value), and in the end generates a confusing mess.

But as I typically recommend, let's not worry about what makes it weird, let's do our best with what we understand. In this case, we can iterate from the given a_1 to bootstrap our way to a_3. Problem solved!

#sequences #logarithms #mathematicalnotation

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[zeroxinski]

honestly i don't feel like it's confusing at all. it doesn't take a lot of experience to know that some subscripts mean indexes of a sequence and some are bits of information about some mathematical object -- in this case, the base of a logarithmic function. there are way more confusing things, such as sin^2(x) and sin^(-1)(x) meaning two entirely different things (the first is sin squared, the second is the inverse function, also known as arcsin). it isn't really the case with subscripts, as in all scenarios of subscript usage it's actually always an indexing function under the hood.

as a side note -- i believe the problem would've been worded a bit better by using the word "sequence", rather than "function", especially since it's defined recursively. Also, defining an element of a sequence in terms of the previous one gives rise to a question: "does this definition hold for the first element?". This latter point is a huge nitpick, but it just goes to show that the problem could've been a bit more precise

[nudecelebs]

Would it be better if it was a(n) instead of a subscript n?? This seems like a non-issue, I don't think this is even an abuse of notation, and I've never come across some issue of "non-operational" vs "operational".

Seems like almost all recursion relations will have some degree of mixing subscript n's with mathematical operations involving n. Is something like a_n = a_(n-1) +n^2 the same "problem"??

Love your vids lol

[mune]

the problem does indeed have horrible notation but it is a pretty easy problem

[abdullah_.]

your videos are one of the greatest :)

[johnlard]

I might be missing something here, but if a_1 means that n=1, that means that log(n-1)/log(n+1) is log(0)/log(2). But log(0) is undefined. So how can a_1=8 or any number for that matter?

[adamantine]

Who wrote the math problem? Please find out and tell them it's terrible and the tell them you can do it better if they pay you $1 million dollars

[indigo]

I mean it’s not particularly hard for anyone with some mediocre experience in high school mathematics ;-;

[aryanshriv]

Sir please try question from an Indian exam called jee advanced