[急] General Maths

Euro Truck Simulator 2 · 由 <MAX » 2010年10月7日 23:40:09 (p#1986118)

(x^3- 1/x)^60 is expanded in ascending powers of x.

(a) Find the general term of the expansion.

(b) Find the coefficient of x^36 in the expansion.

(c) Find the 56th term of the expansion.

有埋過程唔該。 #adore#

由 GE2449~AV36 » 2010年10月8日 18:14:59 (p#1986305)

b.(x^3 - x^-1 ) ^60 = Sum 60Cr (x^3)^(60-r) (x^-1) ^r
For x^36 term, index of x =36
3(60-r) +(-1)r =36
180 -4r =36
4r = 144
r=36

The coefficient = 60C36
Similarly ,you can solve (c)

(c)(x^3 - x^-1 ) ^60 = Sum 60Cr (x^3)^r (x^-1) ^60-r (in ascending power of x)
sub. r=55 to find the 56th term
60C55 (x^3)^55 (x^-1) ^(60-55)
=60C55 x^160

am I correct?

由 GK9141@93A » 2010年10月10日 19:11:03 (p#1987798)

GE2449~AV36 :b.(x^3 - x^-1 ) ^60 = Sum 60Cr (x^3)^(60-r) (x^-1) ^r
For x^36 term, index of x =36
3(60-r) +(-1)r =36
180 -4r =36
4r = 144
r=36

The coefficient = 60C36
Similarly ,you can solve (c)

(c)(x^3 - x^-1 ) ^60 = Sum 60Cr (x^3)^r (x^-1) ^60-r (in ascending power of x)
sub. r=55 to find the 56th term
60C55 (x^3)^55 (x^-1) ^(60-55)
=60C55 x^160

am I correct?

ascending powers of x喎
你應該錯左

a)60Cr．(x^3)^r．(-1/x)^(60-r) (只係睇出黎...)
b)60C24．x^36 ( Set r=24 since 3r+(-1)(60-r)=36 )
c)-60C55．x^160 (Set r+1=56)

即係咁,如果要將(x-1/x)^3排ascending powers of x既話,
咁應該係:
3Cr．(x)^r．(-1/x)^(3-r)
第一項即係r=0,第二項係r=1,咁你會發覺coeff.of x係逐項上升