The discussion centers on calculating \(\sqrt{1/20}\) using the extended binomial theorem with a precision of \(k=4\). The user, Tal, attempts the calculation but arrives at an incorrect result of approximately 0.72. The error is identified as a simple sign mistake in the application of the binomial expansion formula, specifically in the terms involving \((-19/20)^k\). Correcting this sign error will yield the accurate result.
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You made a simple sign mistake somewhere, it seems.talolard said:Homework Statement
Calculate [tex]\sqrt{1/20}[/tex] using the extended binomial theormem. (a precision of k=4 is enough)
The Attempt at a Solution
[tex]\sqrt{1/20}= (1 + (-19/20) )^{1/2}= \sum( choose (1/2,k)*(-19/20)^k) = 1- 1/2*19/20-1/8*361/400+1/16*6589/8000 = 0.72...[/tex] is wrong.
Homework Statement
Where is my mistake?
Thanks
Tal