Question 1000816: This is at the end of our chapter where we learned about arithmetic and geometric sequences and the binomial theorem. The question is: Expand the binomial in the difference quotient and simplify. I'm given [f(x+h)-f(x)] divided by h, I'm then given f(x)=x cubed. I don't get how this relates to series, sequences, their sums, or finding the Nth term, if you could explain the connection as well, I would appreciate it so much.
Found 2 solutions by josgarithmetic, KMST:
Answer by josgarithmetic(39618)   (Show Source):
You can put this solution on YOUR website! "... and the binomial theorem." You mostly need to expand that part in the difference quotient, specifically this part of the expression:
 and refer directly to the binomial theorem formula to be really formal about this. To be simpler about this,  .
Answer by KMST(5328)  (Show Source):
You can put this solution on YOUR website! 
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.
 is the slope of the line AB that passes through points
 and  of the graph of  .
As you decrease  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 is the function
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