using Fortran.90

(a) Write a program to compute the convergent infinite geometric series = 2 Calculate the true percent relative error (8.) and approximate percent relative error (.) defined by true value -- approximation E, 100% true value E present approximation - previous approximation 100% present approximation Use &, & as stopping criterion for the loop where &, is the desired percent relative error. Here assume this value to be 10-4 (correct result to 5 significant digits). (b) Write the result to a file with the first column for number of terms in the series used followed by the values of the computed series, Et, and & (c) Use the intrinsic subprogram cpu_time() to compute the cpu time taken for the computation. (d) Consider another convergent series that alternates harmonically and converges to natural log of 2. (-2)** = In 2 For the same value of & as in (a), compare if this series converges faster than that in (a). (a) Write a program to compute the convergent infinite geometric series = 2 Calculate the true percent relative error (8.) and approximate percent relative error (.) defined by true value -- approximation E, 100% true value E present approximation - previous approximation 100% present approximation Use &, & as stopping criterion for the loop where &, is the desired percent relative error. Here assume this value to be 10-4 (correct result to 5 significant digits). (b) Write the result to a file with the first column for number of terms in the series used followed by the values of the computed series, Et, and & (c) Use the intrinsic subprogram cpu_time() to compute the cpu time taken for the computation. (d) Consider another convergent series that alternates harmonically and converges to natural log of 2. (-2)** = In 2 For the same value of & as in (a), compare if this series converges faster than that in (a)