limiting series question. (1 Viewer)

[barbernator]

can anyone help please? http://exampaper.goodluckwith.us/test/hs/y12/maths/4U/2010SydneyGrammarTrial.pdf

last part last question. cheers

 

[Carrotsticks]

 

[lolcakes52]

Okay, got this. So you can show the error is
Now it is evident the each term is less than the previous. With a little bit of justification, we can say that because of the decreasing size of each term in this error sequence the first time is a pretty good approximation of the error sequence in general. ie




But 3^2 is approximately equal to 2^3

So the error is approximately

 

[RealiseNothing]

That's a surprisingly easy question 8 for Grammar.

 

[barbernator]

haha loving line 3.

 

[lolcakes52]

Damn carrot, your solution is so much better!

 

[barbernator]

Okay, got this. So you can show the error is
Now it is evident the each term is less than the previous. With a little bit of justification, we can say that because of the decreasing size of each term in this error sequence the first time is a pretty good approximation of the error sequence in general. ie




But 3^2 is approximately equal to 2^3

So the error is approximately

you have your signs the wrong way around and it didnt really answer the question.

 

[asianese]

That's a surprisingly easy question 8 for Grammar.

It's easy if you know how to proceed. I doubt many people would know to replace the 9, 11, 13...with all 7s...

 

[math man]

i put it in to series notation, series notation makes shit easier

 

[Carrotsticks]

It's easy if you know how to proceed. I doubt many people would know to replace the 9, 11, 13...with all 7s...

You just have to be on the constant look-out for 'clues'.

For example the final answer I had to acquire was a closed form (nice single expression) whereas what I had was some sort of open infinite summation. My 'clue' was the fact that the only relationship (in the HSC Syllabus) that draws a connection between an infinite series and a closed form, is the Limiting Sum expression. So I 'forced' the series to become a limiting sum (justified via means of an inequality), and then proceeded to compute the sum as per usual.

 

[lolcakes52]

you have your signs the wrong way around and it didnt really answer the question.

Well, everything I said is right.... but I didn't answer the question fully.