Help with part (f) of an inequality problem

[nokia8650]

http://img295.imageshack.us/img295/2538/q1qj1.th.jpg

http://img410.imageshack.us/img410/307/a12ku8.th.jpg

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