Sum An a series and |An| cnverges to 0. If the partial sum Sn (A1+A2+...+An) is...

Sum An a series and |An| cnverges to 0. If the partial sum Sn (A1+A2+...+An) is bounded, is the partial sum Sn' of all absolute value of An (|A1|+|A2|+...+|An|) also bounded?

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Colby Messinger answered 2 years ago

Alternating Series Test. Let (an) be a sequence satisfying (i) a1 ≥ a2 ≥ a3 ≥...

Alternating Series Test. Let (an) be a sequence satisfying (i) a1 ≥ a2 ≥ a3 ≥ · · · ≥ an ≥ an+1 ≥ · · · and (ii) (an) → 0. Show that then the alternating series X∞ n=1 (−1)n+1an converges using the following two different approaches. (a) Show that the sequence (sn) of partial sums, sn = a1 − a2 + a3 − · · · ± an is a Cauchy sequence Alternating Series Test. Let (an) be...

P(A1) = 0.2, P(A2) = 0.25 A1 and A2 are independent Find P(A1C ∩ A2) Please...

P(A1) = 0.2, P(A2) = 0.25 A1 and A2 are independent Find P(A1C ∩ A2) Please add a venn diagram if possible Thanks in advance!

The prior probabilities for events A1 and A2 are P(A1) = 0.50 and P(A2) = 0.45....

The prior probabilities for events A1 and A2 are P(A1) = 0.50 and P(A2) = 0.45. It is also known that P(A1 ∩ A2) = 0. Suppose P(B | A1) = 0.20 and P(B | A2) = 0.05. If needed, round your answers to three decimal digits. (a) Are A1 and A2 mutually exclusive? - Select your answer -YesNoItem 1 Explain your answer. The input in the box below will not be graded, but may be reviewed and considered by...

Starting with the expression for Pr[A1 + A2], show that for three events Pr[A1 + A2...

Starting with the expression for Pr[A1 + A2], show that for three events Pr[A1 + A2 + A3] = Pr[A1] + Pr[A2] + Pr[A3] − Pr[A1A2] − Pr[A1A3] − Pr[A2A3] + Pr[A1A2A3]

Question in graph theory: 1. Let (a1,a2,a3,...an) be a sequence of integers. Given that the sum...

Question in graph theory: 1. Let (a1,a2,a3,...an) be a sequence of integers. Given that the sum of all integers = 2(n-1) Write an algorithm that, starting with a sequence (a1,a2,a3,...an) of positive integers, either constructs a tree with this degree sequence or concludes that none is possible.

Let f: X→Y be a map with A1, A2⊂X and B1,B2⊂Y (A) Prove f(A1∪A2)=f(A1)∪f(A2). (B) Prove...

Let f: X→Y be a map with A1, A2⊂X and B1,B2⊂Y (A) Prove f(A1∪A2)=f(A1)∪f(A2). (B) Prove f(A1∩A2)⊂f(A1)∩f(A2). Give an example in which equality fails. (C) Prove f−1(B1∪B2)=f−1(B1)∪f−1(B2), where f−1(B)={x∈X: f(x)∈B}. (D) Prove f−1(B1∩B2)=f−1(B1)∩f−1(B2). (E) Prove f−1(Y∖B1)=X∖f−1(B1). (Abstract Algebra)

covert the schema into 3NF. TableC (a1,a2,a3,a4,a5) functionally dependencies: a1 --> {a2,a3,a5} a4 --> {a1,a2,a3,a5} a3...

covert the schema into 3NF. TableC (a1,a2,a3,a4,a5) functionally dependencies: a1 --> {a2,a3,a5} a4 --> {a1,a2,a3,a5} a3 -->{a5} Answer: Relation1: Relation2:

What is Corr[A1, A2] where A1 equals B1 minus B2, and A2 equals B2 minus B3and...

What is Corr[A1, A2] where A1 equals B1 minus B2, and A2 equals B2 minus B3and we are given that Bi ∼ Ber(p) for all i in {1,2}?

Let A = {a1, a2, a3, . . . , an} be a nonempty set of...

Let A = {a1, a2, a3, . . . , an} be a nonempty set of n distinct natural numbers. Prove that there exists a nonempty subset of A for which the sum of its elements is divisible by n.

| | a1 | a2 | |----|------|------| | b1 | 0.37 | 0.16 | | b2...

| | a1 | a2 | |----|------|------| | b1 | 0.37 | 0.16 | | b2 | 0.23 | ? | 1. What is ?(?=?2,?=?2)P(A=a2,B=b2)? 2. Observing events from this probability distribution, what is the probability of seeing (a1, b1) then (a2, b2)? 3. Calculate the marginal probability distribution, ?(?)P(A). 4. Calculate the marginal probability distribution, ?(?)P(B).

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