0
What is a sequence that converges to 0 but the series diverges?
Wiki User
∙ 11y ago
harmonic series 1/n .
Wiki User
∙ 11y ago
Add your answer:
Earn +20 pts
What properties of a function can be discovered from its Maclaurin series?
Yes. If the Maclaurin expansion of a function locally converges to the function, then you know the function is smooth. In addition, if the residual of the Maclaurin expansion converges to 0, the function is analytic.
Why are they called fibonaci numbers?
The series 0, 1, 1, 2, 3, 5, 8, 13... is called the Fibonacci series because it was his book that introduced the series to Western mathematicians. Unlike modern interpretations of the sequence, The Liber Abaci started the sequence at 1.
What is the sequence 11235812?
The Fibonacci sequence. The Fibonacci Sequence is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... The next number is found by adding up the two numbers before it
What numbers come next in this series 0 2 1 3 2 4 3?
The next four number in the sequence are... 4,5,5 & 6
What is infinity times infinity minus infinity?
Firstly, infinity is not a number (at least in lower level mathematics). You must instead use the language of limits to describe infinity. Using limits, a function which diverges to infinity multiplied by a function which diverges to infinity has a product which also diverges to infinity. However, taking this product, and subtracting away a function which diverges to infinity is "of indeterminate form". It might converge to zero, it might be diverge to positive infinity, it might diverge to negative infinity, or it might converge to a constant. In order to figure out which one of these possibilities applies, you must get the indeterminate form into the form infinity divided by infinity or 0/0 and then apply L'Hospital's rule. Edit: Just a pet peeve of mine. It's L'Hôpital, not L'Hospital. Even textbooks don't spell it right.
You've an exam on series what essential things are there to know integral ratio test root test maclaurin Taylor pseries etc Can someone explain?
Let us call a series S, it is hard to put all the notation we need here, because we do not have the proper characters, but I will try. 1. One type of series is a geometries series. It converges if for the sum q^n where n goes from 0 to inginitye, q is stritclty between -1 and 1. 2. Consider an integer N and a non-negative monotone decreasing function f defined on the unbounded interval l [N, ∞). Then the series converges if and only if the integral is finite. If the integral diverges so does the series. 3. Assume that for all n, an> 0. Suppose that there exists r such that the limit as n goes to infinity of |a_n+1/a_n)|=r If r < 1, then the series converges. If r > 1, then the series diverges. If r = 1, the ratio test is inconclusive, and the series may converge or diverge. 4. The root test looks at the limsup of the nth root of |a_n|=r, as n goes to infinity. If r1 it diverges and if r=1 the test tells us nothing
What is the rate of convergence for an iteration method?
The rate of convergence of an iterative method is represented by mu (μ) and is defined as such:Suppose the sequence{xn} (generated by an iterative method to find an approximation to a fixed point) converges to a point x, thenlimn->[infinity]=|xn+1-x|/|xn-x|[alpha]=μ,where μ≥0 and α(alpha)=order of convergence.In cases where α=2 or 3 the sequence is said to have quadratic and cubic convergence respectively. However in linear cases i.e. when α=1, for the sequence to converge μ must be in the interval (0,1). The theory behind this is that for En+1≤μEn to converge the absolute errors must decrease with each approximation, and to guarantee this, we have to set 0
What properties of a function can be discovered from its Maclaurin series?
Yes. If the Maclaurin expansion of a function locally converges to the function, then you know the function is smooth. In addition, if the residual of the Maclaurin expansion converges to 0, the function is analytic.
If sender sends a series of packets to the same destination using 5 bit sequence number .if the sequence number starts with 0 then what is the sequence number after sending 100 packets?
0011
Why are they called fibonaci numbers?
The series 0, 1, 1, 2, 3, 5, 8, 13... is called the Fibonacci series because it was his book that introduced the series to Western mathematicians. Unlike modern interpretations of the sequence, The Liber Abaci started the sequence at 1.
What is the sequence 11235812?
The Fibonacci sequence. The Fibonacci Sequence is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... The next number is found by adding up the two numbers before it
11235813. What is the next number in this sequence?
The answer is 21.Your numerical series is the beginning of a mathematical sequence called Fibonacci Numbers.The first number of the sequence is 0, the second number is 1, and each subsequent number is equal to the sum of the previous two numbers of the sequence itself (i.e. 0, 1, 1, 2, 3, 5, 8, 13, 21, etc.).
What is the name of the sequence this type of sequence work by adding the latest two numbers to get the next one?
The Fibonacci Series 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...
How would one describe a Fibonacci number?
A Fibonacci number, Fibonacci sequence or Fibonacci series are a mathematical term which follow a integer sequence. The first two numbers in Fibonacci sequence start with a 0 and 1 and each subsequent number is the sum of the previous two.
What describes the sequence 1 1 2 3 5 is it arithmetic or geometric?
It is an arithmetic sequence. To differentiate arithmetic from geometric sequences, take any three numbers within the sequence. If the middle number is the average of the two on either side then it is an arithmetic sequence. If the middle number squared is the product of the two on either side then it is a geometric sequence. The sequence 0, 1, 1, 2, 3, 5, 8 and so on is the Fibonacci series, which is an arithmetic sequence, where the next number in the series is the sum of the previous two numbers. Thus F(n) = F(n-1) + F(n-2). Note that the Fibonacci sequence always begins with the two numbers 0 and 1, never 1 and 1.
Is 0 0 0 0 0 0 an arithmetic sequence?
Yes it is.
Prove that the sequence n does not converge?
If the sequence (n) converges to a limit L then, by definition, for any eps>0 there exists a number N such |n-L|N. However if eps=0.5 then whatever value of N we chose we find that whenever n>max{N,L}+1, |n-L|=n-L>1>eps. Proving the first statement false by contradiction.
