Infinite Surds

?  Introduction to Infinite Surds
 
 
?       Definition of a concentrated
- An ir demythologised form whose exact value can only be verbalized using the radical or root symbol is called a surd.
E.g.)  is a surd, because the substantial root of two is irrational.
 
?       The origin of the word
          - In or around 825AD, Al-Khwarizmi who was an Arabic mathematician during the Islamic empire referred to the rational bites as audible and irrational as ultrasonic. Then, the European mathematician, Gherardo of Cremona, adopted the terminology of surds (surdus means deaf or mute in Latin) in 1150. In English language, the surd appeared in the work of Robert Recordes The Pathway to Knowledge, published in 1551.
 
?       The symbol, use of the word radical
   - The radical symbol  depicts surds, with the upper striving above the boldness called the vinculum. Also, a cube root takes the form, which corresponds to a1/3 when expressed using indices. So, all roots can hold on in surd form.
 
?       A definition of distance surds
    - An infinite surd is a never ending irrational number and its exact value would be left in square root form.
E.g.) The general infinite surd an =
 Therefore, a3 =
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
?     The following expression is an example of an infinite surd.




 
 
    Consider this surd as a sequence of terms an where:
                       a1 =
                                  a2 =
                          a3 =   and so on.
 
?        Find a reflection for an+1 in terms of an.
Since a1 =  and a2 =,
a2 can be pen as
Therefore, an+1 =
 
?        The first ten terms of the sequence
line| Surd| Decimal|
a1| | 1.414213562|
a2| | 1.553773974|
a3| | 1.598053182|
a4| | 1.611847754|
a5| | 1.616121207|
a6| | 1.617442799|
a7| | 1.617851291|
a8| | 1.617977531|
a9| | 1.618016542|
a10|  | 1.618028597|
?        Plot the relation between n and an
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