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#1 Re: Formulas » Tests For Divisibility » 2009-11-22 04:26:24

simplyjasper

Test for Divisibility by 7
- Double the last digit and subtract it from the remaining leading truncated number. If the result is divisible by 7, so will be the number
Example: 4991
Steps:
499 - 2(1) = 497
49 - 2(7) = 35
Since 7|35, the number is divisible by 7


Test for Divisibility by 13
- Add four times the last digit to the remaining leading truncated number. If the result is divisible by 13, so will the number
Example: 50661
Steps:
5066 + 4(1) = 5070
507 + 4(0) = 507
50 + 4(7) = 78
7 + 4(8) = 39
Since 13|39, the number is divisible by 13

#2 Formulas » Tests For Divisibility » 2009-11-22 04:19:49

simplyjasper
Replies: 12

First the slightly easier ones...
Definition:
2|10 means 2 divides 10 or 10 is divisible by 2 and leave no remainder

Test for Divisibility by 5
- Check if the last digit is 0 or 5
Example: 123512341325
Since the light digit is 5, the number is divisible by 5

Test for Divisibility by 2
- Check if the last digit is even (0, 2, 4, 6, 8)
Example: 12312348
Since the last digit is 8, the number is divisible by 2

Test for Divisibility by 4
- Check if the last 2 digits is divisible by 4
Example: 123124124
Since 4|24, the number is divisible by 4

Test for Divisibility by 8
- Check if the last 3 digits is divisible by 8
Example: 9798743648
Since 8|648, the number is divisible by 8

Test for Divisibility by 16
- Check if the last 4 digits is divisible by 16
Example: 7849758432
Since 16|8432, the number is divisible by 16

Test for Divisibility by 11
- By subtracting the sum of all the even position of the digit by the sum of all the odd position of the digit
Example: 19203182
Odd sum: (1 + 2 + 3 + 6) = 12
Even sum: (9 + 0 + 1 + 2) = 12
Difference is 0 and 0 is divisible by 11. Hence the digit is divisible by 11...

#3 Re: This is Cool » proof that 2=2.82 thus that algebra has a huge fault » 2009-11-22 03:51:16

simplyjasper

3rd line itself is wrong...
If y = x,

x + y = 2x or 2y not x^2

#4 Re: Help Me ! » Calculus Questions » 2009-11-22 03:42:26

simplyjasper
bobbym wrote:

Hi;

(2) is divergent. But I am having a little trouble proving that.

I was thinking it divergent too...
It's one of the four unseen questions in my paper which consists of more than 30% of our grades =/...

He kinda made the class adopt a phobia in Mathematics

#5 Re: Help Me ! » Lagrange's identity » 2009-11-22 00:56:59

simplyjasper

Isn't it just by using the identity and taking away from both side
(a . b)^2

Or you need to prove the identity before you can use it?

#6 Re: Help Me ! » Lagrange's identity » 2009-11-22 00:34:32

simplyjasper

By Lagrange Identity,

#7 Re: Help Me ! » Need Help With Calc. » 2009-11-21 22:42:44

simplyjasper
ineedhelpwithcalc wrote:

OK, I have loads of questions to do with Calc.

1) I don't completely understand definite integration. Do we only need to use the rectangle/trapezium rules if it specifies a number of portions to cut the area under the function into?
[/math]

Rectangle/Trapezium Rule and there's an additional Simpson's Rule... (Or that's what I have came across through my limited years of studies in Math)
They are usually used for the estimation of an integration and don't usually provide the exact value

How these all came out is due to the Riemann sum, you may wish to read up a little bit on them smile...

#8 Re: Help Me ! » Need Help With Calc. » 2009-11-21 22:36:39

simplyjasper
ineedhelpwithcalc wrote:

2)

(x[sup]2[/sup]) +
(1)

And then I integrate both? What answer should I get?

If you do it your way, it should go







You can check where u made a mistake in your integration and don't do it during your exam smile

#9 Re: Help Me ! » Tough equation to differentiate » 2009-11-20 04:45:55

simplyjasper
BeachRum1962 wrote:

Ok simplyjasper please post your method but I almost had it using soroban's method.

Posted by editing my previous post smile

#10 Re: Help Me ! » Calculus Questions » 2009-11-20 03:57:34

simplyjasper
bobbym wrote:

Hi simplyjasper;

That is what I would have done. That is definitely the way to sum that series, if he doesn't give you full credit than it isn't your fault.

Yeah I think my professor is a little bit psycho... He enjoys seeing us fail his paper smile...
Any answers for (2) and (3)?

#11 Re: Help Me ! » Tough equation to differentiate » 2009-11-20 03:56:17

simplyjasper

I did mine through partial fractions and manage to get the result smile...
You can try mine if you think you are more comfortable with partial fractions...

Solving For Partial Fractions, u will get

Using B(t):

Taking Common Factor:

#12 Re: Help Me ! » Calculus Questions » 2009-11-19 03:22:00

simplyjasper
bobbym wrote:

Hi simplyjasper;

I am not making my point clear.

Shouldn't be no more difficult than differentiation. That is how you get the Maclaurin series for Arctan(x). So if you can form a maclaurin series and you know that Arctan(1) = pi/4 you just put x=1 an you have that series. You have summed it.

This is the series you were given to sum:

This is the maclaurin series for Arctan(x):

Now just put 1 into x and the 2 series are the equal.

Since you know that Arctan(1) = pi / 4 you are done.

Guess that's the only way... I couldn't find anything on the website that prove why is the series going towards to the value except for the fact that when u use 5 values of it u get it corrected to 2 decimal places and if u take 7 u get 3 decimals place and so on...

I'm totally not sure what he wants... I just wrote the series = tan-1(1) = pi/4...
Hopefully i will get some marks for that...

#13 Re: Help Me ! » just came up with a problem » 2009-11-19 03:19:44

simplyjasper

I didn't really came out with the twist... I remembered doing one such problem before haha...
It was in my number theory or algebra module

#14 Re: Help Me ! » Trigonometry » 2009-11-19 03:17:44

simplyjasper

I think there's something wrong with the diagram too...
Still with the information, it is sufficient to solve it..
Basically since ACD is an isosceles triangle, AC and CD is equidistant hence u should be able to get the angle for CAD and ADC

Then u should be able to find angle BAD

Finally, by using sine rule, you should be able to get BC

#15 Re: Help Me ! » just came up with a problem » 2009-11-18 13:36:02

simplyjasper

I think there is a need for restriction?
Things like
- u can't copy only a portion of the 'a's u type
- deleting is counted as 1 operation

Else it is pretty simple smile...

What mathsyperson did was the best
or in another way would be type 4 'a's and do that 11 times

As typing 4 'a's and typing 2 'a's then copy and paste yield 4 operations smile

#16 Re: Help Me ! » Calculus Questions » 2009-11-18 12:55:55

simplyjasper
bobbym wrote:

Hi simplyjasper;

That is the MaClaurin series for Arctan(x) when you plug x=1 into it.

So it is easy to sum:

Arctan(1) = π / 4

So:

Hi Bobby,

Yes this is a well known series that is equals to

However, it's a 10 marks questions, I think he's looking into how did this formula came about...

#17 Help Me ! » Calculus Questions » 2009-11-18 01:24:40

simplyjasper
Replies: 9

Just came back from the Calculus exam and I obviously didn't fair well

Some questions that I had difficulties:

(1) Prove that


(2) Determine whether the following series is absolutely convergent, conditionally convergent or divergent


(3) The function

is defined by

    if   
   and   

or

   if   


Prove that the domain of

 
Is
  continuous on
Justify your answer.

#18 Help Me ! » Fibonacci's Sequence » 2009-11-16 06:18:08

simplyjasper
Replies: 4


How do I prove by limits that this sequence is less than 2 for all values of n?

#19 Re: Help Me ! » Need help in finding this infinite series » 2009-11-16 06:09:52

simplyjasper

Appreciate your reply...
Did you use 'telescoping'? As after a great deal of time and random trial and error,  I did manage to get this partial fractions...

But I doubt I have such a luxury of time during my exam...

I was just wondering is there any technique in helping you find a the relationship faster or even another way of solving the sum of this series

#20 Re: Help Me ! » Expected value of 3 cards dealt » 2009-11-16 06:03:48

simplyjasper

Since this is not Monty Hall....
I don't see why u need to have 1000 end branches...

Considering that every number of different suits yield the same points
First row should only include 1 - 9 pts with probability of 1/13 each and (10, J, Q, K) = 10pts with a probability of 4/13

#21 Re: Help Me ! » cosine values » 2009-11-16 05:49:07

simplyjasper

Firstly approaching such question u should have some basic knowledge such as


There are many ways of solving these questions but I guess this formula would solve any angles

For example:



Another method:
Of course there's other ways such as drawing a right-angle isosceles triangle (that is 2 angles at 45 degrees and 1 angle at 90 degrees)
- the length and breadth would be at 1 unit and the hypotenuse is

by Pythagoras Theorem

A picture can be seen in the website below:
http://www.themathpage.com/aTrig/isosceles-right-triangle.htm


#22 Re: Help Me ! » Need help in finding this infinite series » 2009-11-15 19:19:55

simplyjasper
bobbym wrote:

Hi simplyjasper;

That is an indefinite summation. For those you must use the summation by parts formula.

To use that formula you must understand both the difference calculus and the summation calculus. Notice that it is very similar to the integration by parts formula.

If it were like this, a definite summation, you would have a few more options.

This one is much easier, is this what you intended?

Yes that is what i'm intending to find. Had no idea how to do that as i'm still new to posting these formula in this forum... How do you approach this question and manage to find it's 1?

#23 Help Me ! » Need help in finding this infinite series » 2009-11-15 04:12:56

simplyjasper
Replies: 5

How should I approach finding the sum of this infinite series

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