Question

Sum of n terms in a harmonic progression

Answer 1

I am asking

Answer 2

do you have a harmonic progression
?

Answer 3

no in general

Answer 4

nope
http://math.stackexchange.com/questions/496116/is-there-a-partial-sum-formula-for-the-harmonic-series

Answer 5

but he ask about Sum of n terms , so integrate might work :D

Answer 6

or that would be approximation ?

Answer 7

how does one integrate a floor function

\[\large \int \limits_1^{\infty}\dfrac{1}{[x] } - \dfrac{1}{x} dx\]

Answer 8

*\[\large \int \limits_1^{\infty}\dfrac{1}{\lfloor x \rfloor } - \dfrac{1}{x} dx\]

Answer 9

by common sense mmm
its descrete so try to make conjecture

Answer 10

but i think we dnt need floor function mmm
1/x it self should be fine approximation

Answer 11

\[\int \limits_1^n \lfloor x\rfloor = 1 + 2 + 3 + \cdots (n-1)\]

?

Answer 12

\[\int \limits_1^{n} \dfrac{1}{\lfloor x\rfloor} dx = \dfrac{1}{1} + \dfrac{1}{2} + \dfrac{1}{3} + \cdots + \dfrac{1}{n-1}\]

Answer 13

hmm

Answer 14

\[\ln n \ne \int \limits_1^{n} \dfrac{1}{\lfloor x\rfloor} dx = \dfrac{1}{1} + \dfrac{1}{2} + \dfrac{1}{3} + \cdots + \dfrac{1}{n-1} \]

Answer 15

lets refare to integration definition