If $0<a<b,$ determine the limit of $\frac{a^{n+1}+b^{n+1}}{a^n+b^n}$
Solution 1:
Hint :
$$0<a<b\Rightarrow 0<\frac{a}{b}<1\Rightarrow (\frac{a}{b})^n\rightarrow 0$$
Solution 2:
big hint: divide the numerator and the denominator through $b^{n+1}$. That is if $n \to \infty$.