$11..$Prove that $1+2^n<msup><mrow><mn>3</mn></mrow><mrow><mi>n</mi></mrow></msup>$ for all $n>2.$

$22$uusing the tree below, answer the questions $($a$)$ to $($e$).$

a$)$ The depth of the tree

b$)$ The ancestors of $x_{24}$

c$)$ The minimal common ancestor of $x_{14}$ and $x_{11},$ of $x_{15}$ and $x_{11}$

d$)$ The subtree generated by $x_2$

e$)$ The frontier of the tree

Using the tree below, answer the questions $($a$)$ to $($e$).$

a$)$ The depth of the tree

b$)$ The ancestors of $x_{24}$

c$)$ The minimal common ancestor of $x_{14}$ and $x_{11},$ of $x_{15}$ and $x_{11}$

d$)$ The subtree generated by $x_2$

e$)$ The frontier of the tree