If `C_1, C_2 , C_3 , C_4` are the coefficients of any consecutive terms in the expansion of `(1+x)^n` , prove that :
`(C_1)/(C_1+C_2) + (C_3)/(C_3+C_4) = (2C_2)/(C_2 + C_3) `

If C_(0), C_(1), C_(2), …, C_(n) are the coefficients in the expansion of (1+x)^(n) , then what is the value of C_(1) +C_(2) +C_(3) + …. + C_(n) ?

If C_(0), C_(1), C_(2),..., C_(n) are binomial coefficients in the expansion of (1 + x)^(n), then the value of C_(0) - (C_(1))/(2) + (C_(2))/(3) - (C_(3))/(4) +...+ (-1)^(n) (C_(n))/(n+1) is

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

If a. b, c and d are the coefficients of 2nd, 3rd, 4th and 5th terms respectively in the binomial expansion of (1+x)^n, then prove that a/(a+b) + c/(c+d) = 2b/(b+c)

If C_(0),C_(1), C_(2),...,C_(n) denote the cefficients in the expansion of (1 + x)^(n) , then C_(0) + 3 .C_(1) + 5 . C_(2)+ ...+ (2n + 1) C_(n) = .