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This question has been making me mad all day! It's in a advanced maths text book and my teacher asked us to do it for homework.
Here's the question:

How many terms of the sequence 4, 3, 2.25, ... can you add before the sum exceeds 12?

Here's my working out:

My working out
The answer I got is n=-2 and it's incorrect. I checked the answer for this question at back of text book and it was n=4. I tried and tried but still got n=-2. Please help!

AugieJavax98
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  • I simply don't believe you. You only have to add the first five terms! The first four add up to 10.9375, the first five to 12.2031. You have struggled all day to fail to discover that! – almagest Apr 06 '16 at 09:43
  • He had to use maths to prove it, not silly trial and error like you suggest – B.Jenkins Apr 06 '16 at 09:51
  • @B.Jenkins What is the point of wasting time with advanced techniques, when you can solve it in 30 seconds with simple arithmetic (which is part of maths)? – almagest Apr 06 '16 at 09:55
  • @almagest My teacher asked to show my working out. – AugieJavax98 Apr 06 '16 at 09:57
  • It is a maths question set to practice skills and to be a challenge, so that you have practised the method to solve harder problems. Trial and error or just adding up is for fools. – B.Jenkins Apr 06 '16 at 09:57
  • @B.Jenkins I support what you're saying! – AugieJavax98 Apr 06 '16 at 10:01
  • @B.Jenkins Encouraging people to use ill-chosen methods does not help them. If you want them to use things like the formulae for the sum of a geometric series, then set a question which requires it! – almagest Apr 06 '16 at 10:01
  • @almagest Stop being stupid, this is a question for practice. A two year old could do it by adding, but this is a question for using the techniques taught, not just adding up. Exam boards often use questions that are simple, but say that you must actually use a certain method or they may make you prove, using a certain method, that the answer is 4. – B.Jenkins Apr 06 '16 at 10:04
  • @B.Jenkins You would be more persuasive if you were less rude! – almagest Apr 06 '16 at 10:07
  • @almagest You would be more persuasive if you said something intelligent. – B.Jenkins Apr 06 '16 at 10:08

3 Answers3

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Hint. From the line $$ 1-\left(\frac34 \right)^n>\frac34 $$ you get $$ \left(\frac34 \right)^n<\frac14 $$ giving $$ n>\frac{\log(1/4)}{\log(3/4)}=4.8\ldots $$ that is $$n=5.$$

Olivier Oloa
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There is an error in the second row of the second column. The inequality should be $$\left(\frac{3}{4}\right)^n <0.25$$

Edit: to be fair there are some other errors after that point, but that's the first one. Remember that dividing for a negative number changes the direction of the inequality

karmalu
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Try subtracting 1 from both sides instead of adding (second column, second row)

Winner
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