The Babylonian algorithm for deducing
Prove that
What will the sequence from the previous problem 61297 be converging towards if we choose
The iterative formula of Heron. Prove that the sequence of numbers
Method of iterations. In order to approximately solve an equation, it is allowed to write
The algorithm of the approximate calculation of
Prove that
The sequence of numbers
a) the sequence
b)
Find the limit of the sequence that is given by the following conditions
We call the geometric-harmonic mean of numbers
We denote it by
Problem number 61322 says that both of these sequences have the same limit.
This limit is called the arithmetic-geometric mean of the numbers
Prove that the sequence
The numbers