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# P2 Binomial - Problem. watch

1. Question from Heinamann P2 Book: p48 Q12 :

The coefficients of the x and x2 terms in the expansion of (1+kx)n are 44 and 924 respectivley. Find the values of the constants k and n.

(Answer in back: n = 22, k = 2)

Can someone explain to me how to do this? The thing is, i arrived at the answer but i dont know why i did because when i carried out the expansion and equated the coefficients with their respective expansions, i acciently left out the 2! value for the x2, but somehow arrived at the answer.
When i re-tried putting in the missing 2!, i did not get the correct answer.

Could someone help me out!
2. (Original post by cherc2005)
Question from Heinamann P2 Book: p48 Q12 :

The coefficients of the x and x2 terms in the expansion of (1+kx)n are 44 and 924 respectivley. Find the values of the constants k and n.

(Answer in back: n = 22, k = 2)
(1 + kx)n
= 1 + nkx + [n(n-1)/2!][kx]2 + ....

nk = 44 => k = 44/n
[n(n-1)/2][k²] = 924
[½n² - ½n]k² = 924
[½n² - ½n][44/n]² = 924
[½n² - ½n][1936/n²] = 924
1936/2 - 1936/2n = 924
1936n - 1936 = 1848n
88n = 1936
n = 1936/88 = 22

k = 44/n = 44/22 = 2
3. (Original post by cherc2005)
Question from Heinamann P2 Book: p48 Q12 :

The coefficients of the x and x2 terms in the expansion of (1+kx)n are 44 and 924 respectivley. Find the values of the constants k and n.

(Answer in back: n = 22, k = 2)

Can someone explain to me how to do this? The thing is, i arrived at the answer but i dont know why i did because when i carried out the expansion and equated the coefficients with their respective expansions, i acciently left out the 2! value for the x2, but somehow arrived at the answer.
When i re-tried putting in the missing 2!, i did not get the correct answer.

Could someone help me out!
1 + nkx + n(n-1)/2 k^2 x^2 + ... = 1 + 44 x + 924 x^2 + ...

So

nk = 44
n(n-1)k^2 = 2 x 924 = 1848

So

n(n-1)/n^2 = 1848/44^2 = 21/22 [cancelling down]

1 - 1/n = 21/22

n = 22

k = 2
4. Thanks, cant believe I forgot to put k2 in! I was putting k instead. Got the right answer now!

Cheers.

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