If `m=.^(n)C_(2)` show that , `.^(m)C_(2)=3.^(n+1)C_(4)`

If m=nC_(2), show that,mC_(2)=3.(n+1)C_(4)

If m=""^(n)C_(2),"then """^(m)C_(2)=

If .^(m)C_(1)=.^(n)C_(2) prove that m=(1)/(2)n(n-1) .

If m= "^nC_2 , prove that "^m C_2 =3xx ^(n+1)C_4 .

If (1+x)^(n)=C_(0)+C_(1)+x+C_(2)x^(2)+...+C_(n)x^(n) show that, C_(0)-2^(2)*C_(1)+3^(2)*C_(2)-...+(-1)^(n)*(n+1)^(2)*C_(n)=0 (n gt 2)

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)

If m=""^(n)C_(2) , then ""^(m)C_(2) is equal to a) 3""^(n)C_(4) b) ""^(n+1)C_(4) c) 3""^(n+1)C_(4) d) 3""^(n+1)C_(3)

If (1+x)^(n)=sum_(r=0)^(n)C_(r)x^(r), show that (C_(0))/(2)+(C_(1))/(3)+(C_(2))/(4)+...+(C_(n))/(n+2)=(n*2^(n+1)+1)/((n+1)(n+2))

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+…+C_(n)x^(n) , show that, (C_(0))/(1)+(C_(1))/(2)+(C_(2))/(3)+…+(C_(n))/(n+1)=(2^(n+1))/(n+1)