[2024/05/16] Infinite multiplication series
[2024/05/16] Infinite multiplication series
- Show that the infinite multiplication
(1+1/1)(1+1/2)(1+1/3)...does not converge.
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Hint:
spoiler
e
Solution:
spoiler
zkfcfbzr solved it
i put everything into ln because i was scared of multiplication
comment
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)
