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Calculus

Hey I'm only in my 4th week of uni and I'm struggling with a couple of my calculus questions. I've posted my attempts at all the questions, but am unsure where to go from there. Could some one please help me on them please ? The questions are 8b and 9 a and b Thank you
Original post by Roxanne18
Hey I'm only in my 4th week of uni and I'm struggling with a couple of my calculus questions. I've posted my attempts at all the questions, but am unsure where to go from there. Could some one please help me on them please ? The questions are 8b and 9 a and b Thank you



For 8b.

You've shown it's true for S2S_2, and looks like you've going for induction.

For your induction step, it's not clear whether you know what you're summing as you've put nothing under the summation signs, and what you have put doesn't look right.

I suggest writing out SN+1S_{N+1} and SNS_N, subtract the latter from the former and see what you get. You should have three terms left.
Hint: You want to show it's >0.
(edited 7 years ago)
Reply 2
Original post by ghostwalker
For 8b.

You've shown it's true for S2S_2, and looks like you've going for induction.

For your induction step, it's not clear whether you know what you're summing as you've put nothing under the summation signs, and what you have put doesn't look right.

I suggest writing out SN+1S_{N+1} and SNS_N, subtract the latter from the former and see what you get. You should have three terms left.
Hint: You want to show it's >0.


Okay thank you, I will have a try at doing this now. I have just realised that I don't have to do it by induction, so would you think an approach like this would be better ? Is it a valid proof ?
Original post by Roxanne18
Okay thank you, I will have a try at doing this now. I have just realised that I don't have to do it by induction, so would you think an approach like this would be better ? Is it a valid proof ?


No.

l=121N+l1424\displaystyle \sum_{l=1}^2\frac{1}{N+l}\not= \frac{14}{24}

Edit: That sum would actually depend on what the value of N is, and is only equal for N=2.


I really do recommend writing out SNS_N and SN+1S_{N+1}, first and last few terms of each, so you can be clear what you're summing.
(edited 7 years ago)

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