(x^(n-1))/(p+qx^(n))

Simplify the following: 1/(1+x^(m-n)+x^(m-p))+(1)/(1+x^(n-p)+x^(n-m))+(1)/(1+x^(n-m)+x^(p-n))

p=sum_(n=0)^(oo) (x^(3n))/((3n)!) , q=sum_(n=1)^(oo) (x^(3n-2))/((3n-2)!), r = sum_(n=1)^(oo) (x^(3n-1))/((3n-1)!) then p + q + r =

Simplify : (1)/(1+x^(m-n)+x^(m-p))+(1)/(1+x^(n-p)+x^(n-m))+(1)/(1+x^(p-m)+x^(p-n)) .

If y=1/(1+x^(n-m)+x^(p-m))+1/(1+x^(m-n)+x^(p-n))+1/(1+x^(m-p)+x^(n-p)) , then (dy)/(dx) is equal to

If y=(1)/(1+x^(n-m)+x^(p-m))+(1)/(1+x^(m-n)+x^(p-m))+(1)/(1+x^(m-p)+x^(n-p)) the (dy)/(dx) is

If P_(n) denotes the product of all the coefficients in the expansion of (1+x)^(n), n in N , show that, (P_(n+1))/(P_(n))=((n+1)^(n))/(n!) .

If lim_(x->1)((x^n-1)/(n(x-1)))^(1/(x-1))=e^p , then p 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 n be a positive interger 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!) .