Thread: Sum

**Ortega** · August 19th 2008, 06:32 AM

Demonstrate:
$ \ \sum\limits_{k = 1}^n {\frac{1}{k}} \ $

**Plato** · August 19th 2008, 07:00 AM

Originally Posted by Ortega

Demonstrate:
$\ \sum\limits_{k = 1}^n {\frac{1}{k}} \$

Please complete the question. Demonstrate what?

**Ortega** · August 19th 2008, 10:36 AM

Originally Posted by Plato

Please complete the question. Demonstrate what?

i wanna say:calculate the sum...

**masters** · August 19th 2008, 11:50 AM

Originally Posted by Ortega

Demonstrate:
$ \ \sum\limits_{k = 1}^n {\frac{1}{k}} \ $

$\sum\limits_{k = 1}^n {\frac{1}{k}} = \frac{1}{1}+\frac{1}{2}+\frac{1}{3}+ \cdot \cdot \cdot + \frac{1}{n}$

This is an infinite series (harmonic series) whose terms are unit fractions.

Look here for more detail: Harmonic series (mathematics - Wikipedia, the free encyclopedia)

**Moo** · August 21st 2008, 06:11 AM

Originally Posted by masters

$\sum\limits_{k = 1}^n {\frac{1}{k}} = \frac{1}{1}+\frac{1}{2}+\frac{1}{3}+ \cdot \cdot \cdot + \frac{1}{n}$

This is an infinite series (harmonic series) whose terms are unit fractions.

Look here for more detail: Harmonic series (mathematics - Wikipedia, the free encyclopedia)

Infinite ?

**masters** · August 21st 2008, 08:11 AM

Originally Posted by Moo

Infinite ?

Sorry! Only if n = $\infty$

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