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FP2 Problem

I don't understand how they got the inequalities for n in the mark scheme for question 6.

http://www.examsolutions.net/papers/solomon/Edexcel/FP1/FP1F.pdf?x65970 *question*

http://www.examsolutions.net/papers/solomon/Edexcel/FP1/FP1FMS.pdf?x65970 *Mark scheme*
Original post by FHL123
I don't understand how they got the inequalities for n in the mark scheme for question 6.

http://www.examsolutions.net/papers/solomon/Edexcel/FP1/FP1F.pdf?x65970 *question*

http://www.examsolutions.net/papers/solomon/Edexcel/FP1/FP1FMS.pdf?x65970 *Mark scheme*


Well the sum of positive numbers is clearly >0 so there's that bound.

Then they consider the thing that varies, which is 6n+1\frac{6}{n+1}. As the sum is for n≥1n \geq 1 that implies n+1≥2n+1 \geq 2 which implies 1n+1≤12⇒6n+1≤3\frac{1}{n+1} \leq \frac{1}{2} \Rightarrow \frac{6}{n+1} \leq 3

Putting these inequalities together gives 0<6n+1≤30 < \frac{6}{n+1} \leq 3

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