For any positive integer `lim_( x -> a) (x^n-a^n)/(x-a) = na^(n-1)`

For any positive integer n, lim_(xtoa)(x^(n)-a^(n))/(x-a)=na^(n-1)

Find the positive integer n so that lim_( x to 3) (x^n-3^n)/(x-3)=27

lim_ (x rarr a) (x ^ (n) -a ^ (n)) / (xa) = n * a ^ (n-1)

For all positive integers n gt 1, { x(x^(n-1) - n,a^(n-1) ) } + a^(n) (n-1) } is divisible by

Find the positive integer n so that lim_(xto3)(x^(n)-3^(n))/(x-3)=27

For all positive integers {x(x^(n-1)-n*a^(n-1)+a^(n)(n-1)} is divisible by

If x and y are positive real numbers and m, n are any positive integers, then prove that (x^n y^m)/((1+x^(2n))(1+y^(2m))) lt 1/4