Consider the function for a positive integer . Prove that

Conclude that by considering the limit of this as .

* Proof. * We recall the binomial theorem,

So, then we calculate,

Taking the limit as of both sides of the equation we conclude,

Skip to content
#
Stumbling Robot

A Fraction of a Dot
#
Use the binomial theorem to prove the formula for the derivative of x^n

Consider the function for a positive integer . Prove that

Conclude that by considering the limit of this as .

* Proof. * We recall the binomial theorem,

So, then we calculate,

Taking the limit as of both sides of the equation we conclude,