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where a, b and e are constants. g and n are obvious from the sum. How can I find the limit of this series as n approaches infinity? I already tried several approaches, but it's always problematic as the "g" is under the square root sign.
where a, b and e are constants. g and n are obvious from the sum. How can I find the limit of this series as n approaches infinity? I already tried several approaches, but it's always problematic as the "g" is under the square root sign.
First lump your constants, putOriginally Posted by Supernova008
where a, b and e are constants. g and n are obvious from the sum. How can I find the limit of this series as n approaches infinity? I already tried several approaches, but it's always problematic as the "g" is under the square root sign., and
then you have:
The sum can be interpreted as a Riemann sum for an integral from 0 to 1 of a continuous function so the limit is:
CB
I am not a university student yet, so pardon my lack of such advanced mathematical knowledge. I am currently researching this riemann sum, but could you tell me why this is so?First lump your constants, put
The sum can be interpreted as a Riemann sum for an integral from 0 to 1 of a continuous function so the limit is:
CB
EDIT: the first term of the sum is (1/n)*sqrt(1/n^2 + m^2)
however, the first term of the riemann sum is 1/n*sqrt(n^2+m^2), right? isn't that an inconsistency?
What does the red text above refer to?EDIT: the first term of the sum is (1/n)*sqrt(1/n^2 + m^2)
however, the first term of the riemann sum is 1/n*sqrt(n^2+m^2) , right? isn't that an inconsistency?
The partitioning points areand
.
(not advanced mathematical knowlege, this was taught in what would now be years 11 or 12 when I was in secondary education)
CB
Yeah sorry, I got it already, thank you very much!What does the red text above refer to?
The partitioning points are
(not advanced mathematical knowlege, this was taught in what would now be years 11 or 12 when I was in secondary education)
CB
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