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Project: midterm
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Kernel: SageMath 10.1

The following cell was generated by GPT-3.5 using this user prompt:

x1 = √ 2, xn+1 = √ 2 + xn.

(a.) Calculate xn for n = 1, 2, 3, . . . , 10 on Sage. Calculate using an appropriate number of decimal places

# Calculate xn for n = 1, 2, 3, ..., 10 using the given formula

n = 10  # Number of iterations

x = sqrt(2)  # Initial value of x

# Perform the iteration for n times
for i in range(1, n + 1):
    x = sqrt(2 + x)  # Update x using the given formula

# Print the final value of x
x
sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(sqrt(2) + 2) + 2) + 2) + 2) + 2) + 2) + 2) + 2) + 2) + 2)