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# P2 - Expansion of (1+px)^n watch

1. Ok, I'm probably just being really stupid, but could someone help me with this?
It's question 2 from Edexcel P2 paper January 2003.

The first 3 terms in the expansion, in ascending powers of x, of (1+px)^n, are 1-18x + 36p^2x^2. Given that n is a positive integer, find the value of n and the value of p.

Thanks
2. 1. Use the binomial expansion: (1 + ax)^n = 1 + anx + [n(n-1)/2!](ax)^2 + ...
2. Compare coefficients of x and x^2
3. Solve those simultaneous equations
3. (1+px)^n = 1 + n(px) + n(n-1)(px)²/2 +...

= 1 + (np)x + (n²p²/2 - np²/2) x² +...

=> np=-18 AND n²p²/2 - np²/2 = 36p²

you have 2 equations in 2 unknowns, so you can find n and p.
4. For some reason binomial expansions doesn't appear until P4 on my syllabus. i.e.) The 3rd pure module on the A-Level Maths syllabus.

However, we do the factor therem stuff.
5. Thanks everyone!
I'll have to pick one of you to give rep too, but the rest of you will have your turn.
6. Ok, I know what I was doing wrong.
Hangs head in shame, it really wasn't a hard question.

Thanks again everyone.
7. (Original post by Goldfish_Wins)
For some reason binomial expansions doesn't appear until P4 on my syllabus. i.e.) The 3rd pure module on the A-Level Maths syllabus.

However, we do the factor therem stuff.
On my OCR board, we have basic binomial expansion where 'n' is an integer for P2. Then slightly more complicated binomial expansion where 'n' is not an integer in P3.

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