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