If `n >= 2` then `3. C_1-4. C_2+5. C_3-...........+1)^(n-1)(n+2)*C_n=`

C_0 - [C_1 -2.C_2+ 3.C_3-……..+(-1)^(n-1).n.C_n] =

Show that C_0 + 3C_1 + 5C_2 + .... +(2n+1) C_n = (n+1)(2^n)

If C_(0), C_(1), C_(2),..., C_(n) denote the binomial coefficients in the expansion of (1 + x)^(n) , then . 1^(2). C_(1) - 2^(2) . C_(2)+ 3^(2). C_(3) -4^(2)C_(4) + ...+ (-1).""^(n-2)n^(2)C_(n)= .

If C_(0), C_(1), C_(2),..., C_(n) denote the binomial coefficients in the expansion of (1 + x)^(n) , then . 1^(2). C_(1) - 2^(2) . C_(2)+ 3^(2). C_(3) -4^(2)C_(4) + ...+ (-1).""^(n-2)n^(2)C_(n)= .

Prove that 1/(n+1)=(.^n C_1)/2-(2(.^n C_2))/3+(3(.^n C_3))/4- . . . +(-1^(n+1))(n*(.^n C_n))/(n+1) .

Prove that 1/(n+1)=(.^n C_1)/2-(2(.^n C_2))/3+(3(.^n C_3))/4- . . . +(-1^(n+1))(n*(.^n C_n))/(n+1) .

1. ^n C_0+4^1. ^n C_1+4^2. ^n C_2 + 4^3. ^n C_3+….+4^n. ^n C_n =

C_0 C_1 + C_1 C_2 + .... + C_(n-1) C_n = (2^n.n.1.3.5... (2n-1))/(n+1)