It is clear that a(n)=2^(1-2^(-n)). In fact, for n=1 this produces 2^(1-1/2)=sqrt(2)=a1 and if it is true for a(n) then a(n+1) = sqrt (2 * 2^(1-2^(-n))) = sqrt(2^(2-2^(-n))) = 2^(1-2^(-(n+1))) (a) clearly 2^(1-2^(-n))<2<3 so the sequence is bounded by 3. Also a(n+1)/a(n) = 2^(1-2^(-n-1) - 1+2^(-n)) = 2^(1/2^n - 1/2^(n+1)) = 2^(1/2^(n+1)) >1 so the sequence is monotonically increasing. As it is monotonically increasing and has an upper bound it means it has a limin when n-> oo (b) 1-1/2^n -> 1 as n->oo so 2^(1-2^(-n)) -> 2 as n->oo
Answer:
You can find quotes at goodreads.com for this title. If you can't find them, two quotes are "There’s no such thing as plain text; there are only codes you understand and codes you don’t." -Tom Pollock “Sometimes, courage is just knowing what you're more afraid of.” -Tom Pollock
In the story "the most dangerous game" the hunt encompasses two types of external conflict that are:
- Man versus Man and,
- Man versus Nature
The external conflict of Man versus man arises between General Zaroff and Rainsford, where Zaroff is fighting for the goal of fun and amusement whereas, Rainsford fight for the goal of escape and survival. Hence, this feud depicts the clash between morality and philosophy. This leads to physical dispute between them in which Rainsford wins, as he has nothing to lose and he was willing to lose his life to win over Zaroff.
In the other conflict of man versus nature, it occurs when Rainsford lays the trap and trails in the jungle, hence nature creates its own natural obstacles.
<em>“The ground grew softer under his moccasins”, “ The vegetation grew ranker, densely”, “Mosquitoes bit him” and “his foot sank into the ooze”.</em>
Rainsford was able to flee to fewer places due to water all around and high rocky cliffs.
