if `(1+x)^(2n)=sumC_rx^r` then `int_(0->2)(C_0+C_2+C_4+..........+C_(2n))dx` equals to:

if (1+x)^(2n)=sum_(0rarr2n)C_(r)x^(r) then int_(0rarr2)(C_(0)+C_(2)+C_(4)+.......C_(2)n)dx

(1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+….+C_(n)x^(n) then C_(0)C_(2)+C_(1)C_(3)+C_(2)C_(4)+…..+C_(n-2)C_(n) is equal to :

(1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+….+C_(n)x^(n) then C_(0)C_(2)+C_(1)C_(3)+C_(2)C_(4)+…..+C_(n-2)C_(n) is equal to :

If (1+x)^n=sum_(r=0)^n C_r x^r , then prove that C_1+2C_2+3C_3+....+n C_n=n2^(n-1)dot .

If (1+x)^n=sum_(r=0)^n C_r x^r , then prove that C_1+2C_2+3C_3+....+n C_n=n2^(n-1)dot .

If C_(0), C_(1), c_(2),...,C_(n) denote the binomial coefficients in the expansion of (1 + x)^(n) , then C_(0) + (C_(1))/(2) + C_(2)/(3) + ...+ (C_(n))/(n+1) or, sum_(r=0)^(n) (C_(r))/(r+ 1)

Let (1 + x)^(n) = sum_(r=0)^(n) C_(r) x^(r) and , (C_(1))/(C_(0)) + 2 (C_(2))/(C_(1)) + (C_(3))/(C_(2)) +…+ n (C_(n))/(C_(n-1)) = (1)/(k) n(n+1) , then the value of k, is

Let (1 + x)^(n) = sum_(r=0)^(n) C_(r) x^(r) and , (C_(1))/(C_(0)) + 2 (C_(2))/(C_(1)) + (C_(3))/(C_(2)) +…+ n (C_(n))/(C_(n-1)) = (1)/(k) n(n+1) , then the value of k, is

If (1+x)^(n)=underset(r=0)overset(n)sumC_(r).x^(r) , then (1+(C_(1))/(C_(0)))(1+(C_(2))/(C_(1))) . . . .(1+(C_(n))/(C_(n-1)))=0

If C_0, C_1, C_2,………C_n are binomial coefficients int eh expansion of (1+x)^n then and n is even, then C_0^2-C_1^2+C_2^2-C_3^2 + ... +(-1) C_n^2 , is equal to