If n is a positive integer then `(1+x)^n=^nC_0 x^0+^nC_1 x^1+^nC_2^2+………+^nC_rx^r= sum _(r=0)

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If n is a positive integer then `(1+x)^n=^nC_0 x^0+^nC_1 x^1+^nC_2^2+………+^nC_rx^r= sum _ If n is a positive integer then `(1+x)^n=^nC_0 x^0+^nC_1 x^1+^nC_2^2+………+^nC_rx^r= sum _
If n is a positive integer then (1+x)^n=^nC_0 x^0+^nC_1 x^1+^nC_2^2+………+^nC_rx^r= sum _(r=0)^n ^... If n is a positive integer then (1+x)^n=^nC_0 x^0+^nC_1 x^1+^nC_2^2+………+^nC_rx^r= sum _(r=0)^n ^...
If n is a positive integer such that `(1+x)^n=^nC_0+^nC_1+^nC_2x^2+…….+^nC_nx^n, for epsilonR`. If n is a positive integer such that `(1+x)^n=^nC_0+^nC_1+^nC_2x^2+…….+^nC_nx^n, for epsilonR`.
Let `(1 + x + x^2)^n=sum_(r=0)^(2n) a_r * x^r` , where n is a positive integer, if we have Let `(1 + x + x^2)^n=sum_(r=0)^(2n) a_r * x^r` , where n is a positive integer, if we have
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If `n gt 1` is an integer and `x!=0,` then `(1 +x)^n-nx-1` is divisible by If `n gt 1` is an integer and `x!=0,` then `(1 +x)^n-nx-1` is divisible by
If n is a positive integer, then `nC_1+nC_2+...+nC_n = 2^n -1`. If n is a positive integer, then `nC_1+nC_2+...+nC_n = 2^n -1`.