Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 2 (P29709/02)  Year 2017  MayJun  (P29709/21)  Q#4
Hits: 95
Question
The sequence of values given by the iterative formula
With initial value , converges to .
i. Determine the value of correct to 2 decimal places, giving the result of each iteration to 4 decimal places.
ii. Determine the exact value of .
Solution
i.
If we can write the given equation and transform it to , then we can find the root of the equation by iteration method using sequence defined as.
We are already given iterative formula as;
If the sequence given by the inductive definition , with some initial value , converges to a limit , then is the root of the equation .
Therefore, if , then is a root of .
We are given initial value .



1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


It is evident that converges to therefore .
The correct to 2 decimal places is .
ii.
It is evident from (i) that can be written as;
We can manipulate this to find the value of .
Comments