How to get the sum of the series: 1 + 1/2 + 1/3 + 1/4 + ... + 1/n?

I understand the answer is going to be 2 because I've worked with series before, but this is the first time doing it on MATLAB.There is going to be a while loop since this is an infinite series that converges to 2.

Here's what I've got but I'm getting nowhere.

ksum = 1;
n = 0;
while ksum <= 2
    n = n + 1;
    ksum = ksum + 1/n;
end

Help, please!

[Alan Stevens]

Err, no! It's the harmonic series and it diverges to infinity (though it does so very slowly). Look up harmonic series on Wikipedia, for example.

[Voss]

That series diverges. https://en.wikipedia.org/wiki/Harmonic_series_(mathematics)

Also, the way your while loop is written, if you initialize n to be 0, then ksum should initially be 0, because if you initialize ksum to be 1, then the first time through the loop you're adding 1 and 1, which does not appear in the series.

[KSSV]

Sum is not 2..how it is 2?

n = 10^5 ; 
s = 0 ; 
for i = 1:n
  s = s+1/i ; 
end
s

[Rajdeep Mattu]

Oh shoot, yeah, you guys are right about that. I thought it converges to 2, but I must've confused it with a different series.

Well to learn MATLAB better, say I wanted to know which kth term would get the sum past some random number, lets say 3, how would someone write a while loop for that?

Answer 1

[KSSV]

n = 10^5 ; 
s = 0 ; 
i = 0 ; 
while s <= 3  % fix the sum here 
  i = i+1 ; 
  s = s+1/i ; 
end
i

Answer 2

[Image Analyst]

Try this:

n = 1000;
denominators = 1 : n;
theTerms = 1 ./ denominators;
seriesSum = sum(theTerms)