Infinite Surds. As we can see there are ten terms of this sequence where is the general term of the sequence when, is the first term of the sequence.

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Infinite Surds

Introduction

a surd is an irrational number that can not be written as a fraction of two integers but can only be expressed using the root sign.

Bellow an example of an infinite surd:

This surd can be turned into a set of particular numbers sequence:

1.414213562

1.553773974

1.598053182

1.611847754

a51.616121207

1.617442799

1.617851291

1.617977531

1.618016542

As we can see there are ten terms of this sequence where is the general term of the sequence when, is the first term of the sequence...Etc.

A formula has been defined for in terms of:

(1)

A graph has been plotted to show the relation between and. And it can be oticed that as long as gets larger, gets closer to a fixed value.

To investigate more about this fixed value we take this equation into consideration as n gets bigger.

n

an-an+1

1

- 0.13956

2

-0.04428

3

-0.01380

4

-0.00427

5

-0.00132

6

-0.00040

7

-0.00013

8

-0.00004