Does this series converge?

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  1. Michael Penn
  2. math
  3. mathematics
  4. number theory
  5. abstract algebra
  6. calculus
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Комментарии
Автор

Theres a another way to solve the [n/(n+1)]^n limit, which imo is slightly quicker.

[n/(n+1)]^n
= [(n+1)/n]^(-n)
= [1+1/n]^(-n)
= [(1+1/n)^n]^-1
As n-> inf, (1+1/n)^n approaches e (one of the definitions of e), so the answer to the limit is just e^-1

Ninja
Автор

I could immediately tell if it converges and limit of the ratio with Stirling approximation.

КириллЙошкин
Автор

That logarithm-ing and L'Hopital is completely unnecessary... It's obviously the reciprocal of the limit definition of e (Euler's).

reevegarrett
Автор

I'm so glad I never needed to use this after college

coolbrotherf