Geometric series

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Notes

For the geometric progression $(1,r)$ we have:

• $$S_n:\eq\sum^n_{k\eq 1}r^{k-1}\eq\frac{1-r^n}{1-r}$$ (with first term $n\eq 1$, as is our convention (see: sequence))

Thus for a general geometric progression, $(a,r)$ we have:

• $$S_n:\eq\sum^n_{k\eq 1}ar^{k-1}\eq a\sum^n_{k\eq 1}r^k{-1}\eq a\frac{1-r^n}{1-r}$$

See also

• Geometric distribution
• Arithmetic series