If `P_n` denotes the product of all the coefficients of `(1+ x)^n and 8! P_(n+1)=9^8 P_n` then `n` is equal to

If P_(n) denotes the product of all the coefficients of (1+x)^(n) and 9!P_(n+1)=10^(9)P_(n) then n is equal to

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 the coefficients ""^nC_4, ""^nC_5, ""^nC_6 of (1 +x)^n are in A.P. then n is equal to

If P_(n) denotes the product of first n natural numbers, then for all n inN.

If ""^(n)C_(x) = 56 and ""^(n)P_(x) = 336 , then n is equal to

A player tosses a coin and score one point for every head and two points for every tail that turns up. He plays on until his score reaches or passes n. P_(n) denotes the probability of getting a score of exactly n. The value of P_(n)+(1//2)P_(n-1) is equal to

If p a n d q are positive, then prove that the coefficients of x^pa n dx^q in the expansion of (1+x)^(p+q) will be equal.

The combinatorial coefficients ""^(n – 1)C_(p) denotes

If ""(n)C_(0), ""(n)C_(1), ""(n)C_(2), ...., ""(n)C_(n), denote the binomial coefficients in the expansion of (1 + x)^(n) and p + q =1 sum_(r=0)^(n) r^(2 " "^n)C_(r) p^(r) q^(n-r) = .

Let a_n=16 ,4,1, be a geometric sequence. Define P_n as the product of the first n terms. Then the value of 1/4sum_(n=1)^oo P_n^(1/n) is _________.