With usual notations find the value of `3.C_1 + 5.C_2 + 7.C_3 + ……….+n` terms

Find the value of 5C_3 + 4C_2

With usual notations prove that C_0 + 3.C_1 + 3^2.C_2 + ………..+3^n .C_n = 4^n

With usual notations prove that 2.C_0 + 7.C_1 + 12.C_2 + ……..+(5n + 2).C_n = (5n + 4).2^(n-1)

With usual notations prove that C_1+2.C_2x + 3.C_3x^2 + ……+2n.C_(2n) x^(2n - 1) = 2n (1 + x)^(2n -1)

The value of 1^2.C_1 + 3^2.C_3 + 5^2.C_5 + ... is

With usual notations prove that C_1/C_0 + 2. C_2/C_1 + 3.C_3/C_2 + ……+n.(C_n)/(C_(n-1)) = (n(n +1))/(2) Hence prove that (15C_1)/(15C_0) + 2.(15C_2)/(15C_1) + 3. (15C_3)/(15C_2) +……..+ 15. (15C_15)/(15C_14) = 120

The value of 4{ C_1 +4. C_2 +4^2 C_3 + ... +4^(n-1)} is

Find the value of C_0 - [C_1 -2.C_2+ 3.C_3-……..+(-1)^(n-1).n.C_n]

If C_o, C_1, C_2 ....,C_n C denote the binomial coefficients in the expansion of (1 + x)^n, then 1^3. C_1 + 2^3 . C_2 + 3^3 .C_3 + ... + n^3 .C_n, =

With usual notation in Delta ABC, the numerical value of ((a+b+c)/(r_(1)+r_(2)+r_(3))) ((a)/(r_(1))+(b)/(r _(2))+ (c)/(r_(3))) is