- Show that the infinite multiplication
(1+1/1)(1+1/2)(1+1/3)...does not converge.
this post was submitted on 16 May 2024
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Hint:
spoiler
eSolution:
spoiler
zkfcfbzr solved iti put everything into ln because i was scared of multiplication
https://gmtex.siri.sh/fs/1/School/Extra/Maths/Qotd%20solutions/2024-05-16_telescoping-multiplication.html
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Was wondering about that hint - read it after my solution then tried coming up with another that made the product like (1 + 1/n)^n, but the best I was able to manage was proving that the product is larger than e - an impressive feat since it takes a whopping two terms to get that large... Thought it might be something with writing the product like lim (n → ∞) Π (k = 1 to n) (1 + (n/k)/n), but was never able to figure out a way to do anything with that either.i added the solution to the post, i didnt see the multiplication before someone mentioned it, but yeah if we put it to the power of e it will telescope again, which is clearly the main character of this sub at this point (jk)