IB Maths Tutor - Sydney (2 Viewers)

Drongoski · Oct 26, 2013

IB Maths(HL) November 2011 Exam Paper 2

Q12 (b)

$a_1, a_2, a_3 \cdots $ are terms of a geometric sequence with common ratio $ r \neq 1 .\\ \\ $show that: $\\ \\ (a_1 - a_2)^2 + (a_2 - a_3)^2 + (a_3 - a_4)^2 + \cdots + (a_n - a_{n+1})^2 = \frac {a_1^2 (1-r)(1-r^{2n})}{1+r}$

Will post solution later.

Drongoski · Oct 27, 2013

Proof:

$a_i = a_1r^{i-1}\\ \\ (a_i - a_{i+1})^2 = (a_1 r^{i-1} - a_1 r^i)^2 = a_1 ^2 (r^{i-1} )^2 (1-r)^2 \\ \\ \therefore \sum _{i=1} ^n (a_i - a_{i+1})^2 = \sum _{i=1} ^n a_1 ^2 (r^2)^{i-1} (1-r)^2 = a_1 ^2 (1-r)^2 \sum _{i=1} ^n (r^2)^{i-1} \\ \\ = a_1 ^2 (1-r) ^2 \times \left [ \frac {1((r^2)^n - 1)}{r^2 - 1} \right ] $ (a geometric sum) $ \\ \\ = \frac {a_1 ^2 (1-r)(1-r)(r^{2n} - 1)}{(r-1)(r+1)} = \frac {a_1 ^2 (1-r)(1 - r^{2n})}{1+r}$

QED

SpiralFlex · Nov 9, 2013

Bump! To what extent do IB examiners ask when it comes to series [divergence/convergence] (What is considered a tough question?)

Drongoski · Nov 10, 2013

I think it is about the standard of UNSW Maths 1231/1241.

obliviousninja · Dec 12, 2013

BUMP. this guy knows his content.

Drongoski · Jan 5, 2014

obliviousninja said:
BUMP. this guy knows his content.

Are you sure?

Squar3root · Jan 18, 2014

BAMP!!!!!!!!

Drongoski · Jan 19, 2014

Ha thanks $\sqrt$

iJimmy · Jan 21, 2014

Drongoski · Jan 23, 2014

((&))

obliviousninja · Feb 4, 2014

...........

nerdasdasd · Feb 5, 2014

He knows his stuff. Highly recommended

Drongoski · Feb 6, 2014

Thank you nerdo. Very much appreciated.

Drongoski · Jul 24, 2014

My IB Maths HL student got a 7 for the subject last year. This is a matter of great satisfaction for me, of course.

Temptation is to take credit for it. Fact is 90% of the success is due to her own ability and effort.

Drongoski · Aug 28, 2014

If your son or daughter needs help, please don't leave it too late.

Drongoski · Sep 4, 2014

If you need help in your IB Maths, I can help you. Have been tutoring IB Maths for 7 years now.

Drongoski · Sep 16, 2014

If your son or daughter is planing to do the IB Diploma Programme next year, please make sure he/she has the necessary foundation to undertake the Mathematics next year - be it Maths Studies (SL), Maths (SL) or Maths (HL). I'm often distressed for students who struggle in their Maths simply because they are ill-equipped for the course. Now is a good time to get started; to remedy any gaps in his/her maths foundation. The course is so demanding that you need all the time you have in Years 11 and 12 just to cope with the course.

Some schools are beginning their course in Term 4 of Year 10. I think this head start is a good idea as, the schools are able to comfortably complete the course by Term 3 of Year 12.

Drongoski · Oct 8, 2014

With 6 of my 1-on-1 students about to take their exams soon, I'll be able to accept new students, both for the IB and the HSC.

Drongoski · Nov 24, 2014

I'm now able to take a few more highly-motivated Maths students - both for the IB and the HSC(but not General Maths).

Lessons at your place, always. Students from and around Epping especially welcome.

Drongoski · Dec 10, 2014

If you are currently struggling or just want to do better, coming summer break is the best time to get help - when you can put in more guided work without the pressure of assessments and assignment deadlines.

IB Maths Tutor - Sydney (2 Viewers)

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