(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find [itex]\int^{2}_{1}x^{-2}[/itex]dx. Hint: Choose x[itex]^{*}_{i}[/itex] to be the geometric mean of x[itex]_{i-1}[/itex] and x[itex]_{i}[/itex] (that is, x[itex]^{*}_{i}[/itex] = [itex]\sqrt{x_{i-1}x_{i}}[/itex]) and use the identity

[itex]\frac{1}{m(m+1)}[/itex] = [itex]\frac{1}{m}[/itex] - [itex]\frac{1}{m+1}[/itex]

3. The attempt at a solution

First off I am very confused by x[itex]^{*}_{i}[/itex] and the term geometric mean. Of the 70 questions prior to this question x[itex]^{*}_{i}[/itex] = x[itex]_{i}[/itex] but in this question x[itex]^{*}_{i}[/itex] is the square root of.... Yeah I am confused by that too. Could someone please explain how to go about solving this question? I know I have to use the sum of limits as suggested by my notes, but I am not sure where to start.

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# Homework Help: Finding integral using sum of limits?

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