Question

limit n tend to infinity (n+1/n+3)^n the sequences is converge or diverge..?

Answer 1

\[(n+\frac{1}{n}+3)^n\]
?

Answer 2

limit n tends to infinity (n+3/n+1)^n this is question

Answer 3

plz ans this question

Answer 4

This is a long problem. First, we need to let y = given. then take natural log both sides. The steps are similar to prove the definition of e. Please see the PDF for steps. Thanks.
Hint: To find the limit of a function, say if you have no idea how to proceed, plus some number in to approximately the limit. In this case,
x = 1000 => (1003/1000)^1000 = 7.359622545
x = 1000000 => (1000003/1000001)^1000000 = 7.389041321
If you know e ~ 2.71828182845904523536028747135266249775724709369995...,
you can guess the answer could be e^2. To achieve the answer, there is one way to do: to take ln both sides.

Answer 5

Here is the PDF.