Usually the questions tell you what some number, but not sure how to start with this one, any help appreciatedShow that by putting that if the sequence defined by
converges, it will converge to
That gives you solve that for x.
IF this sequence converges, then and each of those limits is of the same sequence and so is equal to x. This is, by the way, a well known iterative method for finding square roots. In fact, it is often known as the "Babylonian method"!
Methods of computing square roots - Wikipedia, the free encyclopedia
The simpler thing to do is just multiply the entire equation, , by 2x.
Clearly not, since you were told that this sequence was supposed to converge to !
Is this correct?
By the way, there is a slight inaccuracy in the problem, related to the fact that they did not give you .
For any , this recursive sequence converges to .
But if , it converges to .
(And, of course, if N< 0, the sequence does not converge.)