Hello, noles2188!

These are geometric series.

The infinite sum is: .

1) There is an infinite staircase.

Find the total volume of the staircase, given that the largest cube has a side of length 1

and each successive cube has a side whose length is half that of the preceding cube.

We have: .

. . . . . . . .

This is a geometric series with: .

Its sum is: .

2) Show that for all real values of

This is a geomtric series with: .

Its sum is: .