In general, an Engel expansion with constant terms is a geometric series.

He expressed the solution to the problem as an infinite geometric series, whose sum was 4/3.

The following table shows several geometric series with different common ratios:

Now life gets tricky: these numbers are in a simple geometric series.

The terms on the left make a geometric series, and we know that converges.

This will be needed in an geometric series with ratio -4.

The first equality is given by the formula for a geometric series in each term of the product.

His silver work had smooth surfaces and was based on the geometric series.

The sum of a geometric series is itself a result even older than Euler.

Above we have used the standard mathematical formula for the sum of a geometric series.