1.

I need to prove that $\displaystyle (x_n)_{n\ge1}$ converges. Normally i'd know how to prove this (with Weierstrass theorem) but this one's a bit different :-s.

2.

In this problem i need to prove that $\displaystyle (x_n)_{n\ge1}$ converges to 2. This translates to $\displaystyle f_n(x_n)=x^{n}_{n}+\ln{x_n}=2^n \to x^{n}_{n}+\ln{x_n}-2^n=0$