Geometric sequences and sums. Infinite geometric series

General rule of geometric sequence can be written by this formula, where $b_1$ - the first term, $q$ - the factor between the terms, $n$ - the number of term.  $$b_n=b_1\cdot q^{n-1}$$
To sum up the terms of an geometric sequence we use this formula: $$\displaystyle S_n=\frac{b_1(q^n-1)}{q-1}$$
If we have geometric sequence, where $-1<q<1$ and $n$ goes to infinity, then it is called infinity geometric serie and sum of it can be calculated by this formula: $$S_n=\frac{b_1}{1-q}$$

Last time edited 2019-01-20

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