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3. numerical analysis let xn be a sequence of positive numbers...

# Question: numerical analysis let xn be a sequence of positive numbers...

###### Question details

(Numerical Analysis)

Let xn be a sequence of positive numbers converging to zero. Show the following:

(a) If xn+1 = x2n, xn converges to 0 quadratically.

(b) If xn+1 = 1xn, xn converges to 0 linearly.2

(c) If xn+1 = n−n, xn converges to 0 superlinearly.