Exercises¶

1. • Question
   • Answer

   Write a fruitful function sumTo(n) that returns the sum of all integer numbers up to and including n. So sumTo(10) would be 1+2+3...+10 which would return the value 55. Use the equation (n * (n + 1)) / 2.

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   def sumTo(n): # your code here

   (ex_5_7)

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   from test import testEqual def sumTo(n): result = (n * (n + 1)) / 2 return result # Now lets see how well this works t = sumTo(0) print("The sum from 1 to 0 is",t) t = sumTo(10) print("The sum from 1 to 10 is",t) t = sumTo(5) print("The sum from 1 to 5 is",t)

   (q7_answer)

2. Write a function areaOfCircle(r) which returns the area of a circle of radius r. Make sure you use the math module in your solution.

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   from test import testEqual def areaOfCircle(r): # your code here t = areaOfCircle(0) testEqual(t,0) t = areaOfCircle(1) testEqual(t,math.pi) t = areaOfCircle(100) testEqual(t,31415.926535897932)

   (ex_5_8)

3. • Question
   • Answer

   Rewrite the function sumTo(n) that returns the sum of all integer numbers up to and including n. This time use the accumulator pattern.

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   def sumTo(n): # your code here

   (ex_5_13)

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   def sumTo(n): sum = 0 for i in range(1,n+1): sum = sum + i return sum # Now lets see how well this works t = sumTo(0) print("The sum from 1 to 0 is",t) t = sumTo(10) print("The sum from 1 to 10 is",t) t = sumTo(5) print("The sum from 1 to 5 is",t)

   (q13_answer)

4. Write a function called mySqrt that will approximate the square root of a number, call it n, by using Newton’s algorithm. Newton’s approach is an iterative guessing algorithm where the initial guess is n/2 and each subsequent guess is computed using the formula: newguess = (1/2) * (oldguess + (n/oldguess)).

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   (ex_5_14)

5. • Question
   • Answer

   Write a function called myPi that will return an approximation of PI (3.14159...). Use the Leibniz approximation.

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   (ex_5_15)

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   def myPi(iters): ''' Calculate an approximation of PI using the Leibniz approximation with iters number of iterations ''' pi = 0 sign = 1 denominator = 1 for i in range(iters): pi = pi + (sign/denominator) sign = sign * -1 # alternate positive and negative denominator = denominator + 2 pi = pi * 4.0 return pi pi_approx = myPi(10000) print(pi_approx)

   (q15_answer)

6. Write a function that takes in input 10 numbers and returns the minimum, the sum, the maximum, and the average.