Question

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.

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
If (xn) is a sequence of nonzero real numbers and if limn→∞ xn = x where...
If (xn) is a sequence of nonzero real numbers and if limn→∞ xn = x where x does not equal zero; prove that lim n→∞ 1/ xn = 1/x
Suppose {xn} is a sequence of real numbers that converges to +infinity, and suppose that {bn}...
Suppose {xn} is a sequence of real numbers that converges to +infinity, and suppose that {bn} is a sequence of real numbers that converges. Prove that {xn+bn} converges to +infinity.
If (xn) ∞ to n=1 is a convergent sequence with limn→∞ xn = 0 prove that...
If (xn) ∞ to n=1 is a convergent sequence with limn→∞ xn = 0 prove that lim n→∞ (x1 + x2 + · · · + xn)/ n = 0 .
Let (sn) ⊂ (0, +∞) be a sequence of real numbers. Prove that liminf 1/Sn =...
Let (sn) ⊂ (0, +∞) be a sequence of real numbers. Prove that liminf 1/Sn = 1 / limsup Sn
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 α be a fixed positive real number, α > 0. For a sequence {xn},...
) Let α be a fixed positive real number, α > 0. For a sequence {xn}, let x1 > √ α, and define x2, x3, x4, · · · by the following recurrence relation xn+1 = 1 2 xn + α xn (a) Prove that {xn} decreases monotonically (in other words, xn+1 − xn ≤ 0 for all n). (b) Prove that {xn} is bounded from below. (Hint: use proof by induction to show xn > √ α for all...
Prove: If x is a sequence of real numbers that converges to L, then any subsequence...
Prove: If x is a sequence of real numbers that converges to L, then any subsequence of x converges to L.
Let (sn) be a sequence. Consider the set X consisting of real numbers x∈R having the...
Let (sn) be a sequence. Consider the set X consisting of real numbers x∈R having the following property: There exists N∈N s.t. for all n > N, sn< x. Prove that limsupsn= infX.
Problem 1 Let {an} be a decreasing and bounded sequence. Prove that limn→∞ an exists and...
Problem 1 Let {an} be a decreasing and bounded sequence. Prove that limn→∞ an exists and equals inf{an}.
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.  
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT