You are here:

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

All Answers

Answers by Expert:

Ask Experts


Scott A Wilson


I can answer almost anything that is sent in. If I can't, I'll let you know, but I don't expect that to happen much.


I have known about number theory since the mid 80's. I have answered over 250 questions on Number Theory with this software. Altogether, I have answered over 8,500 questions in mathematics.

You're looking at it ... I've answered over 8,500 quesitons in mathematics right here.

My credentials are an MS in Mathematics at Oregon State in 1986; I received a BS in Mathematics at the same place in 1984.

Awards and Honors
I graduated with honors in Mathematics when getting my BS degree and my MS degree.

Past/Present Clients
I have assisted many students in mathematics at OSU. Perhaps I have assisted one of you're friends in math on a computer somewhere else, but you don't even know... That would be late last night, perhaps with thousands of miles between us ... Then again, if you're in Washington, so am I ...

©2017 All rights reserved.