Reference no: EM13820068

Question 1. Write a function monexp(n) that returns the partial sum

Me(N) = ΣNk=1 (-1)k/k2.

Question 2. Representing a fraction as a list of two ints, e.g., 2/3 is represented as [2,3], write a function norm() that takes a list of two ints and returns a normalised form, e.g., norm( [-9, 12] ) returns [-3,4].

Question 3. Representing a complex number as a list of two floats, e.g., 2 + 3i be¬comes [2,3], write functions cmul 0 and cdiv() that multiplies and divides two complex numbers (in our representation).

Question 1. Write a function nprimes (n) that returns the number of prime numbers less than n.

Question 2. Write a function pprimes(n) that returns the product of the first n prime numbers.

Question 3. Write a function euprod(n) that returns the partial product
Π(1-1/p2)
p prime<n

Question 4. A positive integer is called square-free if it is not divisible by any perfect square other than 12. Write a function issquarefree (q) that returns True if q is square-free and False otherwise.

Question 5. A positive integer is called a perfect number if it is the sum of all its factors. Write a function isperfect(q) that returns True if q is perfect and False otherwise. Note: you may not simply check the input against known perfect numbers.

• No import is allowed (and similar builtins: exec, execf ile, __import_).

• Your program must not produce spurious output (i.e. no print statements please). Please clean up your debugging and test cases before submitting.