perplexus.info :: Sequences : Precision counts!

Precision counts! (Posted on 2019-05-12)

Let a(k)=(pi)^(.5^k)
Evaluate the expression a(k)-1 for the following values of k: 0, 1, 2, 3 , 10, 20, 50, 100.
Find the smallest k for which the expression is negative
Specify your estimate of results’ accuracy.

See The Solution Submitted by Ady TZIDON

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

re: 1st attempt - not complete

| Comment 3 of 4 |

(In reply to 1st attempt - not complete by Kenny M)

The expression a(k)-1 is never negative

Absolutely correct, this is the right answer.

Having said that, one should try to show how close to zero one can get - and that is of course dependant on the degree of precision in the initial represetation of "pi" and on the scope of one's computing device while dealing with "long" numbers.

I admit that my wording was "lame" and the problem deserves a better presentation.

@Charley - I never considered the negative k - My intention was to find out how close to zero your computation arrives-i.e.

due to calculating dificulties at what k your computer says ZERO, clearly not NEGATIVE.

Edited on May 12, 2019, 10:10 am

Posted by Ady TZIDON on 2019-05-12 10:02:23

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