Write a program that first get the value of a positive integer N (where N> 0) from the user. It then computes the double number 2 using the following series. Use a looping structure. All divisions are real, floating point divisions. Z=1+(1/2) + (1/3) + (1/4)+...+(1/N) Sample Session Microsoft Visual Studio Debug Console Enter a positive integer: 10 - 2.92897 Problem 2: Write a program that asks the user to input a positive integer x. The program then computes and displays the value. of the floating point number 2 using the following formula: (All divisions should be real, floating point divisions). Use afor looping structure. 2 = Microsoft Visual Studio Debug Console Enter a positive integer: 2 Z 3.53804 1 1 x x+1 x+2 Note that the program should NOT allow the user to input a value Problem 4: Write a program that generates a table showing the angle 8 (in radians), from 0 to 2m in the step of 1/4, and the corresponding values for sin(8) and cos). Moreover, prove the identity that sin(8) + cos(8) 1 for each value of 8. Hint: Declare and initialize as const double PI- 3.14159; Use a for loop with theta (angle) varying from 0 to 2*, with end of iteration expression incrementing theta by/4. Use sin(theta) and costheta) functions from library to get the values of sin(theta) and costheta), respectively. The angle theta should be in radians. Use cout.precision (5); cout