Hello My name is Ryley and i well be your scribe for today.

before we start my computer doesn't like using the greater than (>),less than(<) signs so when you see &lt or &gt they mean &lt = less than
&gt = greater than

Infinite Geometric Series

Terms to know

Geometric sequence
-a geometric sequence is a sequence where each term aster the first is found by multiplying the previous term by a common ratio.

An example could be 2, 4, 8, 16, 32 ...., 131072 where the common ratio is 2.

Infinite Sequence
-contains an endless amount of numbers in the domain.

An example could be 3, 9, 27, 81,........ with no final term, it is infinite.

Infinite Geometric Series
-is the sum of all terms in an Infinite Geometric Sequence

-if |r| < 1 , then we have a convergent series, this means that the terms are getting smaller which also means that you can calculate a sum.

-if |r| > 1 , then we have a divergent series, this means that the terms in the sequence are becoming larger and you cannot calculate the sum of the terms.

The Infinite Geometric Series Formula is.

to be able to use this formula the sequence must be convergent (|r|< 1).

Example

36 + 6 + 1 + ......

to find "r" take the second term and divide it by the first term
t2
t1

because |r| is less than 1 you can find the sum.

using this formula find the sum.Subtract the denominators by making them the same

next bring the denominators on top and cross multiply. (they have already been flipped)

which gives you...


So that's how to find the sum in a infinite Geometric series.