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

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Rajdeep Mattu
Rajdeep Mattu on 7 Jul 2020
Answered: Image Analyst on 7 Jul 2020
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!

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Benjamin
Benjamin on 7 Jul 2020
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
KSSV on 7 Jul 2020
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
Rajdeep Mattu on 7 Jul 2020
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?

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Answers (2)

KSSV
KSSV on 7 Jul 2020
Edited: KSSV on 7 Jul 2020
n = 10^5 ;
s = 0 ;
i = 0 ;
while s <= 3 % fix the sum here
i = i+1 ;
s = s+1/i ;
end
i

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Image Analyst
Image Analyst on 7 Jul 2020
Try this:
n = 1000;
denominators = 1 : n;
theTerms = 1 ./ denominators;
seriesSum = sum(theTerms)

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