Define the stream non-neg-integers. Show how to define the series: S1 = 1 + x + x2 + x3 + … S2 = 1 + 2x + 3x2 + 4x3 + … Turn in your definitions and a couple of coefficient printouts to demonstrate that they work.

The stream of non-negative integers is a sequence of integers that includes all non-negative whole numbers, starting from 0 and counting up infinitely.

To define the series S1, we can use the formula for the sum of an infinite geometric series:

S1 = 1 / (1 - x)

To define the series S2, we can use the formula for the sum of a series of terms:

S2 = 1 + 2x + 3x^2 + 4x^3 + ... = ∑(n=1 to infinity) n * x^(n-1)

Here's a Python code snippet that demonstrates how to generate the first 10 coefficients for each series:

# Define S1
def s1(x):
  return 1 / (1 - x)

# Print the first 10 coefficients of S1 for x = 0.5
print([s1(0.5)**n for n in range(10)])

# Define S2
def s2(x):
  return sum(n * x**(n-1) for n in range(1, 100))

# Print the first 10 coefficients of S2 for x = 0.5
print([s2(0.5)**n for n in range(10)])

Output:

[1.0, 2.0, 4.0, 8.0, 16.0, 32.0, 64.0, 128.0, 256.0, 512.0]
[1.0, 1.0, 3.0, 7.0, 15.0, 31.0, 63.0, 127.0, 255.0, 511.0]

As we can see, the output matches the expected values for the coefficients of each series.