1. Consider the sequences defined as follows.(an)
=(12,13,23,14,24,34,15,25,35,45,16,26,36,46,56,17, . . .),(bn)
=(n2(−1)n)= (−1,4,−9,16, . . .).(i)...
1. Consider the sequences defined as follows.(an)
=(12,13,23,14,24,34,15,25,35,45,16,26,36,46,56,17, . . .),(bn)
=(n2(−1)n)= (−1,4,−9,16, . . .).(i) For each sequence, give its lim
sup and its lim inf. Show your reasoning; definitions are not
required.(ii) For each sequence, determine its set of subsequential
limits. Proofs are not required.
(1 point) The three series ∑An, ∑Bn, and ∑Cn have terms
An=1/n^8,Bn=1/n^5,Cn=1/n. Use the Limit Comparison...
(1 point) The three series ∑An, ∑Bn, and ∑Cn have terms
An=1/n^8,Bn=1/n^5,Cn=1/n. Use the Limit Comparison Test to compare
the following series to any of the above series. For each of the
series below, you must enter two letters. The first is the letter
(A,B, or C) of the series above that it can be legally compared to
with the Limit Comparison Test. The second is C if the given series
converges, or D if it diverges. So for instance,...
Prove that the correctness of the following properties of the
given recursive sequences.
a) Given the...
Prove that the correctness of the following properties of the
given recursive sequences.
a) Given the sequence P(1) = 1, P(n) = 2∗P(n−1) for all n ≥ 1,
prove that P(n) = 2n−1 for all n ≥ 1
b) Given the sequence P(1) = 1, P(2) = 1, P(3) = 1, P(4) = 1,
P(n) = P(n − 2) + P(n − 4) for all n ≥ 5, prove that P(n) = P(n −
1) for all even positive integers...