For a positive integer `n`, if the mean of the binomial coefficients in the expansion of `(a+b)^(2n-3)` is `16 `, then `n` is equal to:

If n be a positive integer,show that the algebraic sum of thenumerical coefficients in the expansion of (3x-2y)^(n) is 1 .

If n be positive integer , show that the algebraic sum of the numerical coefficients in the expansion of the (3x-2y)^(n) is 1 .

If n is a positive integer,then the coefficient of x^(n) in the expansion of ((1+2x)^(n))/(1-x) is

If r gt 1, n gt2 are positive integers and the coefficients of (r+2) th and 3rd terms in the expansion of (1+x)^(2n) are equal, then n is equal to-

The sum of the coefficients in the expansion of (6 x-5 y)^(n) where n is a positive integer, is

If n be a positive integer and P_(n) denotes the product of the binomial coefficients in the expansion of (1+x)^(n), prove that (P_(n+1))/(P_(n))=((n+1)^(n))/(n!)

If n be a positive integer and P_n denotes the product of the binomial coefficients in the expansion of (1 +x)^n , prove that (P_(n+1))/P_n=(n+1)^n/(n!) .