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দেখান যে: ^mC1+^(m+1)C2+^(m+2)C3+…….+^(m...

দেখান যে: ^mC_1+^(m+1)C_2+^(m+2)C_3+…….+^(m+n-1)C_n=^nC_1+^(n+1)C_2+^(n+2)C_3+… +^(n+m-1)C_m | ...

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Using binomial theorem (without using the formula for sim nC_(r)), prove that ^nC_(4)+^(m)C_(2)-^(m)C_(1)^(n)C_(2)=^(m)C_(4)-^(m+n)C_(1)^(m)C_(3)+^(m+n)C_(2)^(m)C_(2)-^(m+n)C_(3)^(m)C_(1)+^(m+n)C_(4)

The value of ^n C_1+^(n+1)C_2+^(n+2)C_3++^(n+m-1)C_m is equal to (a)^m+n C_(n-1) (b)^m+n C_(n-1) (c)^mC_(1)+^(m+1)C_2+^(m+2)C_3++^(m+n-1) (d)^m+1C_(m-1)

Prove that ^nC_(0)^(n)C_(0)-^(n+1)C_(1)^(n)C_(1)+^(n+2)C_(2)^(n)C_(2)-...=(-1)^(n)

Prove that mC_(1)^(n)C_(m)-^(m)C_(2)^(2n)C_(m)+^(m)C_(3)^(3n)C_(m)-...=(-1)^(m-1)n^(m)

Evaluate |{:(""^(m)C_(1),""^(m)C_(2),""^(m)C_(3)),(""^(n)C_(1),""^(n)C_(2),""^(n)C_(3)),(""^(p)C_(1),""^(p)C_(2), ""^(p)C_(3)):}|

^(n)C_(m)+^(n-1)C_(m)+^(n-2)C_(m)+............+^(m)C_(m)