Sequences and progressions

# 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) S_{6} if a_{n} = 2^{n}

b) S_{5} 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 €

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