If (1-x^(3))^(n)=underset(r=0)overset(n)...

If `(1-x^(3))^(n)=underset(r=0)overset(n)(sum)a_(r)x^(r)(1-x)^(3n-2r)`, then the value of `a_(r)`, where `n in N` is

`.^(n)C_(r)*3^(r)`

`.^(n)C_(3r)`

`.^(n)C_(r-1)2^(r-1)`

`.^(n)C_(r)2^(r)`

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let underset(r=0)overset(2010)(sum)a_(r)x^(r)=(1+x+x^(2)+x^(3)+x^(4)+x^(5))^(402) and underset(r=0)overset(2010)(sum)a_(r)=a, then the value of ((underset(r=0)overset(2010)(sum)r.a_(r))/(underset(r=0)overset(2010)(sum)a_(r))) is equal to____.

Statement-1: If underset(r=1)overset(n)(sum)r^(3)((.^(n)C_(r))/(.^(n)C_(r-1)))^(2)=196 , then the sum of the coeficients of powerr of xin the expansion of the polynomial (x-3x^(2)+x^(3))^(n) is -1. Statement-2: (.^(n)C_(r))/(.^(n)C_(r-1))=(n-r+1)/(r) AA n in N and r in W .

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AAKASH INSTITUTE ENGLISH-BINOMIAL THEOREM-Assignment (section-B)

If in the expansion of (1 +x)^(m) (1 - x)^(n) , the coefficients ...
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the value of x , for which the 6th term in the expansions of[2^log2sqr...
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If (1-x^(3))^(n)=underset(r=0)overset(n)(sum)a(r)x^(r)(1-x)^(3n-2r), t...
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Let (1+x^2)^2(1+x)^n=sum(k=0)^(n+4)ak x^k. If a1, a2 and a3 are in ari...
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The coefficient of x^1007 in the expansion (1+x)^(2006)+x(1+x)^(2005)+...
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underset(r=0)overset(n)(sum)(-1)^(r).^(n)C(r)[(1)/(2^(r))+(3^(r))/(2^(...
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In the expansion of (x +a)^(n) the sum of even terms is E and that ...
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The sum of the last eight coefficients in the expansion of (1 + x)^16 ...
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The coefficient fo x^(3) y^(4) x^(5) in the expansion of (xy + yz +...
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In the expansion of (3x+2y-z)^(8), the coefficients of x^(2)y^(3)z^(3)...
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If n is ann integer greater than 1, then a-^(n)C(1)(a-1)+.^(n)C(2)(a...
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(C(0))/(1)+(C(1))/(2)+(C(2))/(3)+ . . . .+(C(100))/(101) equals
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2C0+2^2/2 C1+2^3/3 C2+.............+2^11/11 C10 =?
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The coefficient of x^(n) in the polynomial (x+""^(2n+1)C(0))(X+""^(2n+...
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If C(r) stands for .^(n)C(r)=(n!)/(r!n-r!) and underset(r=1)overset(n)...
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If a(n) = sum(r=0)^(n) (1)/(""^(n)C(r)) , find the value of sum(...
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If x + y = 1, prove that underset(r=0)overset(n)sum r.^(n)C(r) x^(r ) ...
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underset(r=1)overset(n)(sum)r(.^(n)C(r)-.^(n)C(r-1)) is equal to
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The expression ""^(n)C(r)+4.""^(n)C(r-1)+6.""^(n)C(r-2)+4.""^(n)C(r-...
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If underset(k=0)overset(n)(sum)(k^(2)+k+1)k! =(2007).2007!, then value...
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