Question

In: Advanced Math

Show that the sequence an = (−1)^n doesn’t converge to 1 nor −1. Can it converge...

Show that the sequence an = (−1)^n doesn’t converge to 1 nor −1. Can it converge to anything other than 1 and −1?

Solutions

Expert Solution

Here the given sequence is not converges because it hes two different limit.1 and -1. And is not converges to any other than 1 and -1.that is sequence is not converges to any point. Answer is believe thank you.


Related Solutions

PROOF; COMPLEX ANALYSIS Show that the sequence {z_n} = {z_1, z_2, ...} is said to converge...
PROOF; COMPLEX ANALYSIS Show that the sequence {z_n} = {z_1, z_2, ...} is said to converge to the complex number w if and only if the sequence of real and imaginary parts of z_n converge to the real and imaginary parts of w, repectively. PLEASE DETAILED PROOF IS REQUIRED. THANKS
A sequence {an} is given by: an = n2 - 1, n € N. Show that it is not an arithmetic progression (A.P)?
A sequence {an} is given by: an = n2 - 1,   n € N. Show that it is not an arithmetic progression (A.P)?   
1. Find all the values of x such that the given series would converge. ∞∑n=1 (3x)^n/n^11...
1. Find all the values of x such that the given series would converge. ∞∑n=1 (3x)^n/n^11 The series is convergent from x =     , left end included (enter Y or N): to x =     , right end included (enter Y or N): 2. Find all the values of x such that the given series would converge. ∞∑n=1 5^n(x^n)(n+1) /(n+7) The series is convergent from x= , left end included (enter Y or N): to x= , right end included (enter Y or...
(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
Determine if the following series converge or diverge. If it converges, find the sum. a. ∑n=(3^n+1)/(2n)...
Determine if the following series converge or diverge. If it converges, find the sum. a. ∑n=(3^n+1)/(2n) (upper limit of sigma∞, lower limit is n=0) b.∑n=(cosnπ)/(2) (upper limit of sigma∞ , lower limit is n= 1 c.∑n=(40n)/(2n−1)^2(2n+1)^2 (upper limit of sigma ∞ lower limit is n= 1 d.)∑n = 2/(10)^n (upper limit of sigma ∞ , lower limit of sigma n= 10)
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
Consider the sequence: x0=1/6 and xn+1 = 2xn- 3xn2 | for all natural numbers n. Show:...
Consider the sequence: x0=1/6 and xn+1 = 2xn- 3xn2 | for all natural numbers n. Show: a) xn< 1/3 for all n. b) xn>0 for all n. Hint. Use induction. c) show xn isincreasing. d) calculate the limit.
Check all of the following that are true for the series ∑n=1∞(n−8)cos(nπ)/(n^2). Converge, diverge, integral test,...
Check all of the following that are true for the series ∑n=1∞(n−8)cos(nπ)/(n^2). Converge, diverge, integral test, comparison test, limit comparison, ratio test, and alternation test. Same with ∑n=1∞8^n/((4^n)-1)
3. The Hofstadter Conway sequence is defined by a(1)=a(2)=1 and (for n>2 by) a(n)=a(a(n-1))+a(n-a(n-1)). Write a...
3. The Hofstadter Conway sequence is defined by a(1)=a(2)=1 and (for n>2 by) a(n)=a(a(n-1))+a(n-a(n-1)). Write a function to quickly compute this sequence. >>> [hc(i) for i in range(1,20)] [1, 1, 2, 2, 3, 4, 4, 4, 5, 6, 7, 7, 8, 8, 8, 8, 9, 10, 11]
(1) Show that the set { 1 m + 1 n : m, n ∈ N}...
(1) Show that the set { 1 m + 1 n : m, n ∈ N} is countable. (2) Show that the set {a + b √ 2 : a, b ∈ Q} is countable. (3) Show that the intersection of two countable sets is countable. (4) Show that the set of all irrational numbers is uncountable. (5) Let C = {0, 1, 2, . . . , 9}. Show that the set C ×C × · · · is...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT