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# Quick FP2 question

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1. For this question,

how was I supposed to know that 2/3 wouldn't get cancelled out? I know that you can just try do it in your mind by subbing in values into the equations and seeing if at any point it cancels out but this method is long winded (especially in this case where I'd have to test out 9 equations). I'm just asking for a more efficient method really..

There's not even a pattern in the way they cancel out:

Attachment 525599525605
Attached Images

2. (Original post by creativebuzz)
For this question,

how was I supposed to know that 2/3 wouldn't get cancelled out? I know that you can just try do it in your mind by subbing in values into the equations and seeing if at any point it cancels out but this method is long winded (especially in this case where I'd have to test out 9 equations). I'm just asking for a more efficient method really..

There's not even a pattern in the way they cancel out:

Attachment 525599525605
Scan the lines diagonally, matching up common denominators, and sum along the lines. You need to keep terms until you hit a zero sum.

3. (Original post by ghostwalker)
Scan the lines diagonally, matching up common denominators, and sum along the lines. You need to keep terms until you hit a zero sum.

Why are you matching the denominators?
4. (Original post by creativebuzz)
Why are you matching the denominators?
You're looking for terms that will cancel to zero in the partial sums. They don't have to match - it's just a guide. As long as you can see the diagonals clearly.
5. (Original post by ghostwalker)
You're looking for terms that will cancel to zero in the partial sums. They don't have to match - it's just a guide. As long as you can see the diagonals clearly.
I don't see how that makes it obvious that 2/3 isn't cancelled out
6. (Original post by creativebuzz)
I don't see how that makes it obvious that 2/3 isn't cancelled out
Sum of first diagonal is ....

Sum of second diagonal is ....

Sum of third diagonal is....
and all subsequent ones, until towards the end.

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