Evaluate if the followings are Cauchy sequences or not. (a) an= (-1)n (b) an= (-1)n/n (c)...

Evaluate if the followings are Cauchy sequences or not.

(a) a_n= (-1)ⁿ

(b) a_n= (-1)ⁿ/n

(d) a_n = (cos n)/n

Solutions

Expert Solution

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

Find the number of N digit sequences from the alphabet a, b, c, d with an...

Find the number of N digit sequences from the alphabet a, b, c, d with an even number of a's and an odd number of b's

Let sn be a Cauchy sequence such that ∀n > 1, n ∈ N, ∃m >...

Let sn be a Cauchy sequence such that ∀n > 1, n ∈ N, ∃m > 1, m ∈ N such that |sn − m| = 1/3 (this says that every term of the sequence is an integer plus or minus 1/3 ). Show that the sequence sn is eventually constant, i.e. after a point all terms of the sequence are the same

Show that id D is dense metric space of X and if all cauchy sequences Yn...

Show that id D is dense metric space of X and if all cauchy sequences Yn from a sense set D converge in D then X is complete.

Recall that a sequence an is Cauchy if, given ε > 0, there is an N...

Recall that a sequence an is Cauchy if, given ε > 0, there is an N such that whenever m, n > N, |am − an| < ε. Prove that every Cauchy sequence of real numbers converges.

(a) The n × n matrices A, B, C, and X satisfy the equation AX(B +...

(a) The n × n matrices A, B, C, and X satisfy the equation AX(B + CX) ?1 = C Write an expression for the matrix X in terms of A, B, and C. You may assume invertibility of any matrix when necessary. (b) Suppose D is a 3 × 5 matrix, E is a 5 × c matrix, and F is a 4 × d matrix. Find the values of c and d for which the statement “det(DEF) =...

[02] For n ≥ 1, how many strings of length n using letters a,b,c are there...

[02] For n ≥ 1, how many strings of length n using letters a,b,c are there if the letter a must occur an even number of times?

1-Write the reaction of acidic water with the followings: a-1-Methylcyclopentene b-1-ethyl-3-methylcyclohexene c-isobutene 2.Draw and name a...

1-Write the reaction of acidic water with the followings: a-1-Methylcyclopentene b-1-ethyl-3-methylcyclohexene c-isobutene 2.Draw and name a cyclic alkyne withasix membered ring.

Consider two investments with the following sequences of cash flows: n Project A Project B 0...

Consider two investments with the following sequences of cash flows: n Project A Project B 0 -$167,000 -$158,500 1 $38,500 $90,300 2 $47,400 $47,500 3 $59,300 $16,000 4 $29,900 $20,300 5 $57,300 $26,500 a) Compute the IRR for each investment. b) At MARR = 9%, consider the acceptability of each project. c) If A and B are mutually exclusive projects, which project would you select on the basis of the rate of return on incremental investment?

Poof if a) A is nonsingular b) N(A) = {0} c) rank(A) = n

Find a primitive root for: (a) n = 18, (b) n = 50 (c) n =...

Find a primitive root for: (a) n = 18, (b) n = 50 (c) n = 27, (d) n = 625.

Subjects