Seriously????!!!
If can be expressed as continued fraction, then what is the largest number which is less than or equal to the AM of all the numbers(except 1) in the continued fraction form?
Note: Give your answer to at least 2 decimals.
The answer is 2.68.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
For almost all real numbers x ,the coefficients of the continued fraction of x have a finite geometric mean which is independent of the value of x and it is known as Khinchin‘s Constant .More information about it can be found here .It is approximately equal to 2 . 6 8 .By the AM-GM inequality we know that equality only occurs when each element is same.So answer is 2 . 6 8 .
Sorry if my solution is confusing.