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STEP Support Programme

Step II 2006 Q5

I am doing part (i) but I cannot get the answer to come out to be the soln. I keep getting 3/2(n-1) but the answer is supposed to be 3/2n(n-1)
I simplified the integral to just be the 3 times the integral of x - floor(x) between n and 1 and calculated that as (n-1) * area of a unit triangle * 3 but this doesn't get me the correct answer.
What am I doing wrong?
Thanks and sorry I don't know how to format this properly

I'm pretty sure that's a typo. I also got $\frac{3}{2}(n-1)$ by the same method as you.

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