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
When we're old, wise and grey. Or by the way we portray ourselves, people can learn a lot about us.
<em>'A Supermarket in California' </em>in imagery poem. Allen Ginsberg lists the supermarket items like fruits and foods.
<h3>What is enumeration?</h3>
Enumeration is the depiction of the total or the things that are mentioned by the numbering. The poem is about the supermarket that is located in California where the poet goes to buy the items.
He enumerates the fruit items one by one that he wants to eat and imagines them as a mix of the people and the food, like 'babies in the tomatoes. He imagines and uses illusion to show the presence of the two poets Garcia Lorca and Walt Whitman at the supermarket.
Therefore, the poet enumerates fruits in the supermarket.
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