Mathematico | Mathematico

A graphics artist needs to find the area of the shape formed between the curve

y = {(\frac{5}{4})}^{x}

and the straight lines

x = 0, x = 10, y = 0

Curve with area

In order to do this, she splits the shape up into $10$ rectangles, as below:

Curve with rectangles

Find the sum of the areas of the rectangles.
This estimate is not accurate enough for the artist, and so she instead splits the shape into $20$ rectangles: Find the new estimate for the area of the shape.

Geometric series.