This problem considers the following algorithm                                 It is assumed  is a prescribed (positive) integer. (a) What is the exact value for ? (b) Using MATLAB, if  = 104, one...

This problem considers the following algorithm

It is assumed
 is a prescribed (positive) integer.

(a) What is the exact value for
?

(b) Using MATLAB, if
 = 104, one gets that
 1.4 × 10⁻¹³, if
 = 108, one gets that
 2.2×10⁻⁹, and if
 = 1011, one gets that
 1.3×10⁻⁶. Why is the error getting worse as
 increases? Is there any correlation between the value of
 and the value of?

(c) Use compensated summation to compute this result and compare the values with those given in part (b).