The sum of integers between 1 and n is given by sigman i1 i

The sum of integers between 1 and n is given by sigma^n _i=1 i = n(n+1)/2 Write a Fortran program that prompts the user for n and reports the sum three ways using the algebraic formula above. using a counting loop using a do while loop (The filenames for the three parts should be hw05_01a. f95, hw05_01b. f 95, and hw05_01c.f95.) A common (but not efficient) Taylor series expansion lets us approximate the arctangent function using tan^-1 (x) = sigma^m _n=0 (-1)^n x^2n+1/2n+1 which has m+1 terms and is valid for x in [-1, 1]. The approximation becomes exact asm rightarrow infinity

Solution

hw05_01a.f95

//in this program summation is done based on formula...

PROGRAM summation
     IMPLICIT NONE
     INTEGER n
     print*, \'ENTER THE NUMBER\'
     read*, n
     print*, \'THE NUMBER IS\', n
     PRINT*, sum_n(n) ! etc
    CONTAINS
     RECURSIVE FUNCTION sum_n(N) RESULT(N_sum)
      INTEGER, INTENT(IN) :: N
      INTEGER :: N_sum ! also defines type of fact
       IF (N /= 1) THEN
         N_sum = N + sum_n(N-1)
       ELSE
         N_sum = 1
       END IF
     END function sum_n
    END PROGRAM summation

hw05_01b.f95

//this program is used to find sum using do loop

program looping
implicit none
integer :: count, n, number,sum

print*, \'ENTER THE NUMBER\'
read*, number
print*, \'THE NUMBER IS\', number
n = number
sum = 0
do count=1,n
sum = sum + dble(count)

end do
write (*,*) \' Value of sum is \',sum
stop
end program looping

//program for inverse tan series using taylor series

program infiniteSeries
implicit none
integer :: n = 1
real :: degRad = 3.141592653589793 / 180
real :: atanApprox, atanIntrinsic = 0., mytan = 0., x = 0.

write(*,*)\"Please enter a value in degrees\"
read(*,*) x
x = x * degRad
atanIntrinsic = atan(x)
do n = 1, 10
    mytan = atanApprox(x,n)
    write(*,*) n, mytan
end do
write(*,*) \"Intrinsic function atan() =\", atanIntrinsic
end program infiniteSeries

real function atanApprox(x,n)
implicit none
real :: x, fact ! type of the function fact()
integer :: n, k, a

atanApprox = 0.
do k = 0, n
  
    atanApprox = atanApprox + (-1)**k * x**(2*k+1) / fact(2*k+1)
end do
end function atanApprox

function fact(a)
implicit none
real :: fact
integer :: a, i

fact = 1.
do i = 1, a
    fact = fact * i
end do
end function fact