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Geometric sequences and sums. Infinite geometric series


General rule of geometric sequence can be written by this formula, where [tex]b_1[/tex] - the first term, [tex]q[/tex] - the factor between the terms, [tex]n[/tex] - 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 [tex]-1<q<1[/tex] and [tex]n[/tex] 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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Algebraviews 90answers 0activity 2 mo

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