If the sequence is increasing then it a) converges to its supremum b) diverges c) may...

If the sequence is increasing then it a) converges to its supremum b) diverges c) may converge to its supremum d) is bounded

if S= { 1/n - 1/m: n,m belongs to N } where N is the set of natural numbers then infimum and supremum of S respectively are a) -1and 1 b) 0,1 c)0,0 d)can not be determined

Please explain

Solutions

Expert Solution

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

Determine whether the geometric series converges or diverges. If it converges, find its sum. -1/9 +...

Determine whether the geometric series converges or diverges. If it converges, find its sum. -1/9 + 1/27 - 1/81 + 1/243 - ...

(a) a sequence {an} that is not monotone (nor eventually monotone) but diverges to ∞ (b)...

(a) a sequence {an} that is not monotone (nor eventually monotone) but diverges to ∞ (b) a divergent sequence {an} such that {an/33} converges (c) two divergent sequences {an} and {bn} such that {an + bn} converges to 17 (d) two convergent sequences {an} and {bn} such that {an/bn} diverges (e) a sequence with no convergent subsequence (f) a Cauchy sequence with an unbounded subsequence

Which one of the improper integrals below converges or diverges? [int _a ^b] means integral from...

Which one of the improper integrals below converges or diverges? [int _a ^b] means integral from a to b, we use inf to indicate infinity. a) [int _0 ^1] 1/x dx b) [int _0 ^1] 1/x^(1/2) dx c) [int _0 ^1] 1/x^2 dx d) [int _1 ^inf] 1/x dx e) [int _1 ^inf] 1/x^(1/2) dx f) [int _1 ^inf] 1/x^2 dx g) [int _1 ^inf] lnx / x^2 dx h) [int _1 ^inf] lnx / x dx i) [int _(-inf)...

prove every cauchy sequence converges

Determine if the following series converges or diverges and explain why. 1) 1 - (4/6) +...

Determine if the following series converges or diverges and explain why. 1) 1 - (4/6) + (4/6)^2 - (4/6)^3 + ... 2) 1 - (6/4) + (6/4)^2 - (6/4)^3 + ...

Show that a monotone sequence converges if and only if it is bounded.

Prove that every sequence in a discrete metric space converges and is a Cauchy sequence. This...

Prove that every sequence in a discrete metric space converges and is a Cauchy sequence. This is all that was given to me... so I am unsure how I am supposed to prove it....

Determine if ∑(-1)^n/(4n-7), n=0 to infinity, absolutely or conditionally converges or diverges?

Let (sn) be a sequence that converges. (a) Show that if sn ≥ a for all...

Let (sn) be a sequence that converges. (a) Show that if sn ≥ a for all but finitely many n, then lim sn ≥ a. (b) Show that if sn ≤ b for all but finitely many n, then lim sn ≤ b. (c) Conclude that if all but finitely many sn belong to [a,b], then lim sn belongs to [a, b].

A sequence (xn) converges quadratically to x if there is some Q ∈ R such that...

A sequence (xn) converges quadratically to x if there is some Q ∈ R such that |xn − x| ≤ Q/n^2 for all n ∈ N. Prove directly that if (xn) converges quadratically, then it is also Cauchy.

Subjects