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  3. consider the sequence: x0=1/6 and xn+1 = 2xn- 3xn2

Consider the sequence: x0=1/6 and xn+1 = 2xn- 3xn2 | for all natural numbers n. Show: a) xn< 1/3...

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Question

Advance Math

Consider the sequence: x0=1/6 and xn+1 =2xn- 3xn2 | for all naturalnumbers n.

Show:

a) xn< 1/3 for all n.

b) xn>0 for all n.

Hint. Use induction.

c) show xn isincreasing.

d) calculate the limit.

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