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If is a positive integer write an integral to represent .

Notice that this is a Riemann sum with infinitely many rectangles.

And a Riemann sum with infinitely many rectangles is the Definition of an Integral:
Can you rewrite this as an integral?

 so we can substitute  with .

The represents the infinitely small width of each rectangle.
Now let’s find the height of each rectangle.
Heights, of course, are represented by a function, .
But what is ?

Since is a variable, we will let represent the part of the series that is changing:
This is beginning to look more like an integral: 

We still need to find the bounds of the integral.
The lowest value of is   . Since , the lower bound is .