Question

. A sequence { bn } is defined recursively bn= -bn-1/2, where b1 = 3. (a)...

. A sequence { bn } is defined recursively bn= -bn-1/2, where b1 = 3. (a) Find an explicit formula for the general term of the bn = f(n). (b) Is the sequence convergent or divergent? (c) Consider the series ∑ approaches infinity and n=1 bn.  Is this series convergent or divergent? (d) If it is convergent, find its sum

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Find a general term (as a function of the variable n) for the sequence{?1,?2,?3,?4,…}={45,1625,64125,256625,…}{a1,a2,a3,a4,…}={45,1625,64125,256625,…}. Find a...
Find a general term (as a function of the variable n) for the sequence{?1,?2,?3,?4,…}={45,1625,64125,256625,…}{a1,a2,a3,a4,…}={45,1625,64125,256625,…}. Find a general term (as a function of the variable n) for the sequence {?1,?2,?3,?4,…}={4/5,16/25,64/125,256/625,…} an= Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. (If it diverges to infinity, state your answer as inf . If it diverges to negative infinity, state your answer as -inf . If it diverges without being infinity or negative infinity, state your answer...
6. Let series {an} = 1/(n2 + 1) and series {bn} = 1/n2. Use Limit Comparison...
6. Let series {an} = 1/(n2 + 1) and series {bn} = 1/n2. Use Limit Comparison Test to determine if each series is convergent or divergent. 7. Use Ratio Test to determine if series {an}= (n + 2)/(2n + 7) where n is in interval [0, ∞] is convergent or divergent. Note: if the test is inconclusive, use n-th Term Test to answer the question. 8. Use Root Test to determine if series {an} = nn/3(1 + 2n) where n...
1) The twelfth term of an arithmetic sequence is 118, and the eighth term is 146....
1) The twelfth term of an arithmetic sequence is 118, and the eighth term is 146. Find the nth term. (3 points) 2) A partial sum of a geometric sequence is given. Find the sum. (3 points) 3) Determine wether the given infinite geometric series is convergent or divergent. If the series is convergent, then find its sum. (4 points) a)   b)
Consider a sequence defined recursively as X0= 1,X1= 3, and Xn=Xn-1+ 3Xn-2 for n ≥ 2....
Consider a sequence defined recursively as X0= 1,X1= 3, and Xn=Xn-1+ 3Xn-2 for n ≥ 2. Prove that Xn=O(2.4^n) and Xn = Ω(2.3^n). Hint:First, prove by induction that 1/2*(2.3^n) ≤ Xn ≤ 2.8^n for all n ≥ 0 Find claim, base case and inductive step. Please show step and explain all work and details
Consider the sequence defined recursively by an+1 = (an + 1)/2 if an is an odd...
Consider the sequence defined recursively by an+1 = (an + 1)/2 if an is an odd number an+1 = an/2 if an is an even number (a) Let a0 be equal to the last digit in your student number, and compute a1, a2, a3, a4. (b) Suppose an = 1, and find an+4. (c) If a0 = 4, does limn→∞ an exist?
. Consider the sequence defined recursively as a0 = 5, a1 = 16 and ak =...
. Consider the sequence defined recursively as a0 = 5, a1 = 16 and ak = 7ak−1 − 10ak−2 for all integers k ≥ 2. Prove that an = 3 · 2 n + 2 · 5 n for each integer n ≥ 0
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.  
1. Find the first six terms of the recursively defined sequence Sn=3S(n−1)+2 for n>1, and S1=1...
1. Find the first six terms of the recursively defined sequence Sn=3S(n−1)+2 for n>1, and S1=1 first six terms =
c.) Determine whether the seriesX∞ k=1 k(k^4 + 2k)/(3k 2 − 7k^5) is convergent or divergent....
c.) Determine whether the seriesX∞ k=1 k(k^4 + 2k)/(3k 2 − 7k^5) is convergent or divergent. If it is convergent, find the sum. d.) Determine whether the series X∞ n=1 n^2/(n^3 + 1) is convergent or divergent.
3. Consider the following property: for any ε>0, there exists N∈N so that whenever n≥N,|u_n+1−u_n|<ε. What...
3. Consider the following property: for any ε>0, there exists N∈N so that whenever n≥N,|u_n+1−u_n|<ε. What is the difference between this property and the definition of a Cauchy sequence? Find a convergent sequence which has this property. Find a divergent sequence which has this property. (Hint: can you think of a function f(x) which grows to infinity very slowly? Then try a_n=f(n).
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT