Question

Let {s_n} be a sequence of positive numbers. Show that the condition lim as n-> infinity...

Let {s_n} be a sequence of positive numbers. Show that the condition lim as n-> infinity of (s_n+1)/(s_n) < 1 implies s_n -> 0

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Prove that if (xn) is a sequence of real numbers, then lim sup|xn| = 0 as...
Prove that if (xn) is a sequence of real numbers, then lim sup|xn| = 0 as n approaches infinity. if and only if the limit of (xN) exists and xn approaches 0.
a. Show that if lim sn = infinity and k > 0, then lim (ksn) =...
a. Show that if lim sn = infinity and k > 0, then lim (ksn) = infinity. b. Show that lim sn = infinity if and only if lim (-sn) = -infinity
(1) Show that -infinity to infinity ∫ xdx is divergent. (2) Show that lim t→∞ definite...
(1) Show that -infinity to infinity ∫ xdx is divergent. (2) Show that lim t→∞ definite integral -t to t ∫ xdx = 0. This shows that we cannot define ∫ ∞ −∞ xdx= lim t→∞ definite integral-1 to t ∫ xdx
Question 4 Let a sequence {an}∞ n=1 a sequence satisfying the condition ∀c ∈ (0, 1),...
Question 4 Let a sequence {an}∞ n=1 a sequence satisfying the condition ∀c ∈ (0, 1), ∀n ∈ N, | a_(n+2) − a_(n+1) | < c |a_(n+1) − a_n |. 4.1 Show that ∀c ∈ (0, 1), ∀n ∈ N, n ≥ 2, | a_(n+1) − a_n | < c^(n−1) | a_2 − a_1 |. 4.2 Show that {an}∞ n=1 is a Cauchy sequence
If lim Xn as n->infinity = L and lim Yn as n->infinity = M, and L<M...
If lim Xn as n->infinity = L and lim Yn as n->infinity = M, and L<M then there exists N in naturals such that Xn<Yn for all n>=N
If {sn} is a sequence of positive numbers converging to a positive number L, show that...
If {sn} is a sequence of positive numbers converging to a positive number L, show that √ {sn} converges to √ L. Do not solve using calc but rather an N epsilon proff
Let Sum from n=1 to infinity (an) be a convergent series with monotonically decreasing positive terms....
Let Sum from n=1 to infinity (an) be a convergent series with monotonically decreasing positive terms. Prove that limn→∞ n(an) = 0.
Prove that lim n^k*x^n=0 as n approaches +infinity. Where -1<x<1 and k is in N.
Prove that lim n^k*x^n=0 as n approaches +infinity. Where -1<x<1 and k is in N.
Let (a_n)∞n=1 be a sequence defined recursively by a1 = 1, a_n+1 = sqrt(3a_n) for n...
Let (a_n)∞n=1 be a sequence defined recursively by a1 = 1, a_n+1 = sqrt(3a_n) for n ≥ 1. we know that the sequence converges. Find its limit. Hint: You may make use of the property that lim n→∞ b_n = lim n→∞ b_n if a sequence (b_n)∞n=1 converges to a positive real number.  
Telescoping Series. Let {an} ∞ n=0 be a sequence of real numbers converging to zero, limn→∞...
Telescoping Series. Let {an} ∞ n=0 be a sequence of real numbers converging to zero, limn→∞ an = 0. Let bn = an − an+1. Then the series X∞ n=0 bn converges.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT