sum of the terms of a geometric progression

If we want to add the first k terms of a geometric progression, we need to use this formula:

For example, if we want to add

If |r|< 1, then we can add the infinite terms of a progression with this formula:

For example: 100, 50, 25, …

Exercises:

1.- Calculate:

a) S₆ if a_n = 2ⁿ

b) S₅ if a_n = 3, 9, 27, 81,...

c) S_∞ if a_n = 2^-n

 2.- Juan bought 10 books. He paid 1€ for the first, 2 € for the second , 4 € for the third , ... How much did all books cost?.

Solutions: 1.- a) 126; b) 363; c) 1;

2.- He paid 1023 €