How can I find the first integer n for which the sum of the numbers below is greater than 2.5?

1+1/2+1/3+1/4+...+1/n>2.5

Answer 1

[DGM]

Here's one simple way:

kmax = 10;
n = 1:kmax;
s = cumsum(1./n);
[n' s']

ans = 10×2

1.0000 1.0000 2.0000 1.5000 3.0000 1.8333 4.0000 2.0833 5.0000 2.2833 6.0000 2.4500 7.0000 2.5929 8.0000 2.7179 9.0000 2.8290 10.0000 2.9290

kest = n(find(s>2.5,1,'first'))

kest = 7