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
This is taken from “The Minister’s Black Veil” written by Nathaniel Hawthorne. The minister in this short story is Mr. Hooper, who covers half of his face with a black veil, which gets the community to gossip about him. On his deathbed Reverend Clark lets him keep the veil on his face because he thinks he hides his face because he has committed a crime.
Reverend Clark’s reaction to Father Hooper’s keeping the veil from being removed supports the theme of:
Answer: A. forgiveness
I can’t help if you don’t ask
Answer:
just give the story and I got you
Explanation:
