# Exact value seems to be hard!

Is there any way to find the exact value of $$A_n = 1 + \frac{1}{2} + \frac{1}{3} +...+ \frac{1}{n}$$? And is there a closed form?

Note by Steven Jim
1 year, 1 month ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

This is called the Harmonic series, and there is no closed form. However, the sum $$1 + \frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{n}$$ is approximately $$\log n$$. See the following for more details.

https://en.wikipedia.org/wiki/Harmonicseries(mathematics)

- 1 year, 1 month ago

Thanks! Very much appreciated!

- 1 year, 1 month ago