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MRB Constant V

Marvin Ray Burns 550 Maple
March 23 2012
0

The*MRB*constant = sum((-1)^n*(n^(1/n)-1), n = 1 .. infinity) and sum((-1)^n*(n^(1/n)-1), n = 1 .. infinity) = sum((-1)^n*(n^(1/n)-1), n = 2 .. infinity)

But what can we say about

(∏)(-1)^(n)*(n^(1/(n))-1)?

``

``

Maple does not evaluate it:

evalf(product((-1)^n*(n^(1/n)-1), n = 2 .. infinity))

product: Cannot show that (-1)^n*(n^(1/n)-1) has no zeros on [2,infinity] product((-1)^n*(n^(1/n)-1), n = 2 .. infinity)

 (1)

And perhaps it should not because of the alternating sign;

evalf(product((-1)^n*(n^(1/n)-1), n = 2 .. 10^2))

-0.3908773173e-101

 (2)

evalf(product((-1)^n*(n^(1/n)-1), n = 2 .. 10^3))

-0.7676360791e-1799

 (3)

evalf(product((-1)^n*(n^(1/n)-1), n = 2 .. 10^3+1))

0.5316437097e-1801

 (4)

``

 

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