標題:
發問:
(x^2+3/x)^13 find(x^8的項)
最佳解答:
(a+b)^n = nC0*a^n + nC1*a^(n-1)*b + nC2*a^(n-2)*b^2 + ... + nCn*b^n (x^2+3/x)^13 =1*(x^2)^13 + 13*(x^2)^12*(3/x) + (13*12)/(1*2)*(x^2)^11*(3/x)^2 + ... x^2(13-n) * x^(-n) = x^8 2(13-n)-n = 8 -3n = -18 n = 6 設x^8的項 為a. ax^8 = (13*12*11*10*9*8)/(1*2*3*4*5*6) *(x^2)^(13-6) *(3/x)^6 ax^8 = 1716 *3^6 *x^8 ax^8 = 1250964x^8 ∴a = 1250964 ∴x^8的項 = 1250964 打到好亂,唔好意思 驚你睇唔清,所以highlight 咗:)
其他解答:
Suppose 13Cr (x2)r (3/x)13-r is the term of x8, then: 2r - (13 - r) = 8 3r - 13 = 8 r = 7 Hence then term of x8 is: 13C7 (36) x8 = 1250964 x8
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M1 Queation發問:
(x^2+3/x)^13 find(x^8的項)
最佳解答:
(a+b)^n = nC0*a^n + nC1*a^(n-1)*b + nC2*a^(n-2)*b^2 + ... + nCn*b^n (x^2+3/x)^13 =1*(x^2)^13 + 13*(x^2)^12*(3/x) + (13*12)/(1*2)*(x^2)^11*(3/x)^2 + ... x^2(13-n) * x^(-n) = x^8 2(13-n)-n = 8 -3n = -18 n = 6 設x^8的項 為a. ax^8 = (13*12*11*10*9*8)/(1*2*3*4*5*6) *(x^2)^(13-6) *(3/x)^6 ax^8 = 1716 *3^6 *x^8 ax^8 = 1250964x^8 ∴a = 1250964 ∴x^8的項 = 1250964 打到好亂,唔好意思 驚你睇唔清,所以highlight 咗:)
其他解答:
Suppose 13Cr (x2)r (3/x)13-r is the term of x8, then: 2r - (13 - r) = 8 3r - 13 = 8 r = 7 Hence then term of x8 is: 13C7 (36) x8 = 1250964 x8
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