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

    Cheers.
 
 
 
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