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OCR FP2 Series & Integrals Problem

This chapter is definitely the most irritating in FP2.

Please see the attached image.

For i), would it be sufficient to just say the area of the of the rectangles (from 1 to n) > the area under the graph (from 1 to n+1). I'm really confused how to go about answering these questions without repeating what the question's already given you :s-smilie:.

Similarly, for ii), what else is there to say other than the area of the rectangles (from 2 to n) < the area under the graph (from 1 to n). Again, if I did say this I'd be repeating what the question has already given me - but I'm not sure what's required here for 3 marks!

I'd really appreciate any help or advice on these type of questions :smile:.
Reply 1
In (i), you key point is that the LHS is the total area of the given rectangles, which includes all of the area for the integral, plus some extra.

in (ii), I'd advise drawing a new sketch.
Reply 2
For i) I'd first explain why the area of each of the rectangles is 1/1^2 etc then explain that each of these rectangles is greater in area than the area below the curve of the same width and position. I'd also say that the total width of these rectangles is equal to the width of the integral. That should be enough to get two marks.

For ii) I'd draw a sketch and then write a similar argument to i). It's best to write as much as you can in these questions, even if you think the answer is trivial.
(edited 12 years ago)

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