Geometric Series (Fortran)

Series

This Fortran program computes a geometric series and its running sum. A geometric series has the form:

S_{n} = a + a r + a r^{2} + a r^{3} + \dots + a r^{n - 1}

where $a$ is the first term and $r$ is the common ratio.

Sum Formula

The sum of the first $n$ terms is:

S_{n} = a \frac{1 - r ^{n}}{1 - r}

for $r \neq = 1$ .

Implementation

program geometric_series
    implicit none
    integer, parameter :: dp = kind(1.0d0)
    integer :: n, i
    real(dp) :: a, r 
    real(dp), dimension(:), allocatable :: series, running_sums
    character(len=100) :: filename

    ! Parameters for the geometric series
    a = 1.0_dp     ! First term
    r = 0.5_dp     ! Common ratio
    n = 20         ! Number of terms

    ! Allocate arrays
    allocate(series(n))
    allocate(running_sums(n))

    ! Compute the geometric series and running sums
    series(1) = a
    running_sums(1) = a
    do i = 2, n
        series(i) = series(i-1) * r
        running_sums(i) = running_sums(i-1) + series(i)
    end do

    ! Set filename
    filename = 'geometric_series_running_sum.csv'

    ! Write to CSV file
    open(unit=10, file=filename, status='replace')
    write(10, '(A)') 'Term,Value,Running_Sum'  ! CSV header
    do i = 1, n
        write(10, '(I5,1x,F10.5,1x,F10.5)') i, series(i), running_sums(i)
    end do
    close(10)

    ! Deallocate arrays
    deallocate(series)
    deallocate(running_sums)

end program geometric_series

Key Features

Uses allocatable arrays for dynamic memory allocation
Computes both individual terms and running sums
Outputs results to CSV file
Properly deallocates memory after use
Uses character variables for filenames

Memory Management

The program demonstrates proper memory management by allocating arrays at runtime and deallocating them when done.