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Chapter 5: while loop

Exercise 1

Write a while loop which print numbers from 0 to 20 in increasing order without using the instruction if:

sage: # edit here

Same question but in decreasing order:

sage: # edit here

Exercise 2

What is the below program doing?:

a, b, c = 1, 1, 1
while c < 11 :
    print(c, ": ", b)
    a, b, c = b, a+b, c+1
sage: # edit here

Exercise 3

Using a while loop, write a function orbit_product_of_digits(n) which returns the list of successive iterations of the function which returns the product of digits, that is, [n, product_of_digits(n), product_of_digits(product_of_digits(n)), ..., z] until a computed number z<10 is reached that can be written with only one digit:

sage: # edit here

Can you find a number n such that the length of the orbit is larger than 5?:

sage: # edit here

... larger than 10?:

sage: # edit here

Exercise 4

The Taylor series of sin(x) is

sinx = limn → ∞k = 0n(( − 1)k)/((2k + 1)!)x2k + 1 = x − (x3)/(3!) + (x5)/(5!) − ⋯

Write a function taylor_sin(x) which evaluates the Taylor series neglecting the terms of the sums that are less than 10 − 5 in absolute value:

sage: # edit here

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