The coefficient of in the expansion of is equal to _________. ...

aligned & (1-x)(1-x)^2007(1+x+x^2)^2007 \\ & (1-x)(1-x^3)^2007 \\ & (1-x)( ^2007 C_0- ^2007 C_1(x^3)+ .) aligned General term aligned & (1-x)((-1)^r ^2007 C_r x^3 r) \\ & (-1)^r 2007 C_r x^3 r-(-1)^r 2007 C_r x^3 r+1 \\ & 3 r=2012 \\ & r 20123 \\ & 3 r+1=2012 \\ & 3 r=2011 \\ & r 20...

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The coefficient of x2012 in the expansion of 1x20081xx22007 : null (Mathematics) | DivineJEE

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Mathematics

The coefficient of $x^{2012}$ in the expansion of $(1-x)^{2008}\left(1+x+x^2\right)^{2007}$ is equal to _________.

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For integers n and r let n r nCr ifn ge r ge 0 0 otherwise

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Let A = { 1,3,4,6,9} and B = { 2,4,5,8,10}. Let R be a relation defined on A X B such that R = {( ( a_{1},b_{1} ), ( a_{2},b_{2} )):a_{1} ? b_{2} and b_{1} ? a_{2}}. Then the number of elements in the set R is

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For (2 leq r leq n,binom{n}{r} + 2binom{n}{r - 1} + binom{n}{r - 2} =)

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