Home #1 Mathematics Calculate the following limit ... (Now solved)
Calculate the following limit ... (Now solved) PDF Print E-mail
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Wednesday, 17 December 2008 13:42

Consider the sequence where n runs on numbers, with a fixed x.

Let,

a (n,x) = k (k√x - 1),

where k = 2n.

To what quantity tends a(n,x), where n ->∞ ?

(Just another small problems. Write an algorithm to calculate the square root, using the four basic operations. Calculate the cubic root using a pocket calculator (with the maximum operation is square root). Apply previous method to calculate any root)

Solution.

The sequence,

limn->∞ a (n,x) = limn->∞ (k (k√x - 1))= log x.

where k = 2n.

Now, to calculate the cubic (3) root of n, using a basic calculator with a square root (2), check the answer in Computer section. However, you can press the √x twice and multiply for the number x. Repeat the process until the result does not change.

Using this method, you can calculate the root of quintic from the quartic, and the seventh from the sixth, and so, is easy to see that you can calculate any root.

With no calculator you can use the recurring sequence,

where, xn= n√x

 

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Last Updated on Friday, 19 December 2008 14:52