(1+1/1)(1+1/2)(1+1/3)... does not converge.
Hint:
spoiler
e
Solution:
spoiler
zkfcfbzr solved it
i put everything into ln because i was scared of multiplication
solution
The terms can be rewritten as:
(2/1) * (3/2) * (4/3) * ... * ((n+1)/n) * ...
Each numerator will cancel with the next denominator. In total everything cancels, so the answer is the empty product, 1.
...Wait...
Uhm, ignore that. Rather, consider the products we get when multiplying. We get: 2/1. 6/2. 24/6. Etc. That is, we have:
Π (n = 1 to k) (n+1)/n = (k+1)! / k! = (k+1)k!/k! = k+1
k+1 clearly goes to infinity as k → ∞, so our product diverges to infinity.
Share your cool maths problems.
Complete a challenge:
Post a challenge:
Feel free to contribute to a series by DMing the OP, or start your own challenge series.
