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Number Theory/mathematical limit


What is the limit of this sequence as n tends towards infinity:

1/2 + 1/3 + 1/4 + 1/5 + …. + 1/(n-3) + 1/(n-2) + 1/(n-1) + 1/n

Is the limit +infinity? (I hope not! Not for what I want it for! ) Or is it finite? And why is it whatever value it is? -I mean, how does one work out the limit to such a sequence? Is there a general method?

How do you express the above sequence using standard maths limit notation without the vague “ + … + “ part?

Also: does it ONLY make sense to talk about a mathematical limit like this one “as n tends towards infinity” or can you also rationally talk about a mathematical limit like this one where n is LITERALLY equal to +infinity?

(I already asked this question to Clyde Oliver more than 3 days ago but he hasn't yet responded )

That is an infinite sum, so there is no limit.
The individual terms go to 0, but the sum does not.
Approximating this with an integral gives the integral of 1/x for x going from 1 to infinity.
Since this is ln(x), the ln() of infinity is infinity, so there is no limit.

The value of n can never be infinity, but it only tends towards infinity.
No matter what value is given to n, n+1 is greater.
That is why it is said to be the limit as n tends to infinity.

Number Theory

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Scott A Wilson


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