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A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

It is true in engineering it would be rare to need more than 6 digits but CAS are capable of spitting out millions or even billions of digits. Numerical analysis is one way to determine how reliable those digits that are given are.

The fellow who published .7285058960783131 is making a statement about the accuracy of his answer. We would like to be able to verify it or prove his answer is overoptimistic.

]]>Computers do not always tell us the truth. We have already seen that problems can arise when we multiply by a large number, divide by a small number, subtract 2 nearly equal numbers and more.

When we say n = .08 we are implying that we know the number with a certain accuracy. We are claiming

which means .075 < n < .085

When we say n = .576128 we are implying that we know the number with a certain accuracy. We are claiming

which means .5761275 < n < .5761285

Putting down the answer .7285058960783131 implies that we know this:

which means .72850589607831305 < .7285058960783131 < .72850589607831315

Are we justified in saying that?

]]>and got .7285058960783131.

What do you think of their answer?

]]>What's next?

]]>http://www.mathisfunforum.com/viewtopic … 57#p384157

Post #177. You should see that a minor change produces the recurrence of this thread.

]]>where

is the HurwitzLerchPhi function.

]]>2) I evaluated the integral numerically.

3) I ran the recurrence in the backward direction.

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