Investigating Hard Inequalities: Understanding Part (f)

[nokia8650]

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I am having trouble with the final part of this question - part f; I can do all the previous parts. I have attached the questions and markscheme, and so woulkd appreciate it if someone could just explain part (f) to me!

Thanks a lot.

 

[HallsofIvy]

If (f) is the part you are having trouble with, then presumably you have already proved that 2x_n^2- (2n-1)x- (n+1)= 0 (part (e)). Now you want to find the smallest n such that x_n< n+ 0.05. You could, for example, solve that using the quadrative formula and compare the solutions to n+ 0.05. Have you calculated some values of x_n? What are x_0 x_1, etc.?

 

[nokia8650]

Thanks for the help. I am still confused as to how the markscheme answers have come about which I attached above.

Thanks