Pascal's triangle

[Voltman]

In year 12 methods, do you need to memorise Pascal's Triangle?

[TrueTears]

you should as it is helpful for binomial expansion, to be honest pascals triangle isn't hard to remember anyway

[Voltman]

you should as it is helpful for binomial expansion, to be honest pascals triangle isn't hard to remember anyway

To which row?

[mano91]

you would probably need to know up to Power of 5.
never got any further than that.

[Voltman]

Hmmm...I'll add a big one as a screensaver just in case (15 rows).

[shinny]

I assume you haven't actually noticed the pattern if you're asking this...look at it like this;

                        0 1 0
                       0 1 1 0
                      0 1 2 1 0
                     0 1 3 3 1 0
                    0 1 4 6 4 1 0

Basically, for any row, the number that should be there is the sum of the two numbers surrounding it in the row above. I've put the 0's there to make this more obvious. e.g. For the 5th row, the first number is 1 as 0+1 is 1, second number is 4 as 1+3 if 4 and so on.

As you can see, it's VERY easy to remember for an indefinite number of rows.    

EDIT: Or perhaps you knew this pattern and was just wanting to memorise for time measures? In that case, don't bother. You've got plenty of time to draw this up (you'll never need to go very far down anyway) and drawing it up on the spot according to this pattern is less likely to cause you mistakes than recall errors will.    

[kamil9876]

Or you can just use combinatorics:

e.g:

and you have things cancelling very nicely: plus u don't need to calculate all the rows from 1-6 to get row 7. Plus u can use the fact that it's symmetrical to save almost half the calculation time i.e symmetrical because nCk=nC(n-k).

[IntoTheNewWorld]

I personally think pascal's triangle is better than combinatorics for this purpose, it really doesn't take that long to do quite a few rows, and it's easier (and less prone to errors) to do binomial expansion using a row from pascal's triangle imo.

[Voltman]

EDIT: Or perhaps you knew this pattern and was just wanting to memorise for time measures? In that case, don't bother. You've got plenty of time to draw this up (you'll never need to go very far down anyway) and drawing it up on the spot according to this pattern is less likely to cause you mistakes than recall errors will.    

Yes...I was aware of that pattern.

[shinny]

Well like I said, there's definitely no need to memorise the rows themselves. Just redraw it every time and that's enough.

[TrueTears]

Well like I said, there's definitely no need to memorise the rows themselves. Just redraw it every time and that's enough.

yeap, that's exactly what I do when I do binomial expansion and it's much less prone to error.

[kurrymuncher]

Dont waste your time

[Damo17]

In my opinion, as Shinny said just remember the pattern and you can't go wrong. It would be a waste of time memorising many rows if you know the pattern.