$$(1+\frac{5}{n})^{2n}$$ I need to figure the limit if it converges or state if it goes to $$ \pm\infty $$ or simply "divergent" if it diverges but not to infinity.

From what I can tell as n -> infinity $$\frac{5}{n} -> 0 $$ so would it be the same as evaluating $$(1)^{2n}$$ which would just = 1 ?

or do i need to do some form of squeeze theorem like $$(\frac{5}{n})^{n} <(\frac{5}{n})^{2n} <(1+\frac{5}{n})^{2n}$$


We have





The sequence $$\left(1+\frac an\right)^n$$ converges to $e^a$ as $n\to\infty$. So, your sequence tends to $e^{10}$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.