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Suppose that Newton’s method is applied to find the solution p = 0 of the equation...

Suppose that Newton’s method is applied to find the solution p = 0 of the equation
e^x −1−x− (1/2)x^2 = 0. It is known that, starting with any p0 > 0, the sequence {pn} produced by the Newton’s method is monotonically decreasing (i.e., p0 >p1 >p2 >···)and converges to 0.
Prove that {pn} converges to 0 linearly with rate 2/3. (hint: You need to have the patience to use L’Hospital rule repeatedly. ) Please do the proof.
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