Question 1000816
{{{f(x)=x^3}}}
{{{f(x+h)=(x+h)^3}}}
{{{(f(x+h)-f(x))/h=((x+h)^3-x^3)/h=(x^3+3x^2h+3xh^2+h^3-x^3)/h=(3x^2h+3xh^2+h^3)/h=3x^2+3xh+h^2}}}
I do not see how this relates to series, sequences, their sums, or finding the Nth term either.
I see how this relates to algebra in general, and polynomials in particular, and
I see how this is a sneaky introduction to derivatives,
which would belong in an early calculus lesson.
If the name of your class is pre-calculus, a sneaky introduction to derivatives may be the purpose of this problem.
{{{(f(x+h)-f(x))/h}}} is the slope of the line AB that passes through points
{{{A(x,f(x))}}} and {{{B(x+h,f(x+h))}}} of the graph of {{{f(x)}}} .
As you decrease {{{abs(h)}}} towards zero, points A and B get closer together,
"tending to" being the same point A, and the line AB tends to being the tangent to the curve at A.
The derivative of {{{f(x)}}} is the function
{{{df/dx=d(x^3)/dx=lim(h->0,(f(x+h)-f(x))/h)=lim(h->0,(3x^2+3xh+h^2))=3x^2}}}