Fraction Calculator: 1/2 : 1/3

How bởi vì I calculate this sum in terms of "n"?I know this is a harmonic progression, but I can"t find how to calculate the summation of it. Also, is it an expansion of any giayphutyeuthuong.vnematical function?

1 + một nửa + 1/3 + 1/4 +.... + 1/n


There is no simple closed form. But a rough estimate is given by

$$sum_r=1^n frac1r approx int_1^n fracdxx = log n $$

So as a ball park estimate, you know that the sum is roughly $log n$. For more precise estimate you can refer to lớn Euler"s Constant.

Bạn đang xem: Fraction calculator: 1/2 : 1/3


There is no simple expression for it.

But it is encountered so often that it is usually abbreviated to $H_n$ & known as the $n$-th Harmonic number.

There are various approximations & other relations which you can find in Wikipedia under Harmonic Number or in the question Jose Santos referenced in the comments.

Xem thêm: Trong Ngôn Ngữ Lập Trình Biến Được Xem Là, 10 Ngôn Ngữ Phổ Biến Và 5 Công Dụng Intalents

For example, $$H_n=G_n-(n+1)lfloorfracG_nn+1 floor$$ where $$G_n=fracn+(n+1)!choose n-1(n+1)!$$

But that kind of thing is more of a curiosity than a useful expression!


One can write$$1+frac12+frac13+cdots+frac1n=gamma+psi(n+1)$$where $gamma$ is Euler"s constant và $psi$ is the digamma function.

Xem thêm: Diode Bán Dẫn Có Tác Dụng :

Of course, one reason for creating the digamma function is khổng lồ make formulaelike this true.


Not the answer you're looking for? Browse other questions tagged summation or ask your own question.

how khổng lồ find a sum of numbers in a sequence when some intermediate terms are not taken in to consideration?

Site kiến thiết / hình ảnh sản phẩm © 2022 Stack Exchange Inc; user contributions licensed under cc by-sa. Rev2022.4.21.42004

Your privacy

By clicking “Accept all cookies”, you agree Stack Exchange can store cookies on your device và disclose information in accordance with our Cookie Policy.