Find the limit when n tends to infinity of the following:
Best Answer
Outline: Let $1/n=t$. Using your idea, we first want to find the limit as $t$ approaches $0$ from the right of
$$\frac{\ln\left(\frac{1+2^t}{2}\right)}{t}.$$ L'Hospital's Rule will work nicely for this.
The limit originally asked for will turn out to be $\sqrt{2}$.
Best Answer
Outline: Let $1/n=t$. Using your idea, we first want to find the limit as $t$ approaches $0$ from the right of $$\frac{\ln\left(\frac{1+2^t}{2}\right)}{t}.$$ L'Hospital's Rule will work nicely for this.
The limit originally asked for will turn out to be $\sqrt{2}$.