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(Solved): 1 (a) Find the fifth term in the expansion of (x^(3)-(1)/(2x))^(6) in descending powers of x. (b) Fi ...
1 (a) Find the fifth term in the expansion of
(x^(3)-(1)/(2x))^(6)in descending powers of
x. (b) Find the term independent of
xin the expansion of
(9x-(1)/(3\sqrt(x)))^(18). (c) Find the coefficient of
x^(-18)in the expansion of
(3x+(1)/(x^(2)))^(12). (d) Expand
(2+3x+4x^(2))^(10), up to the term in
x^(3). (e) The coefficient of
x^(2)in the expansion of
(2x+k)^(6)is equal to the coefficient of
x^(5)in the expansion of
(2+kx)^(8). Find
k. (f) The expansion of
(1+kx)^(n)up to and including the term in
x^(3)are
1+36x+66k^(2)x^(2)+hx^(3), where
nis a positive integer. Find the values of
n,kand
h. (a)
(15)/(16)x^(2)(b) 18564 (c) 594 (d)
1024+15360x+124160x^(2)+691200x^(3)+cdots; (e)
(15)/(112)(f)
n=12,k=3,h=5940