Beauty of Series

Infinite Geometric Series

An infinite geometric series, is an infinite series that is geometric. A series with infinite as its greatest value.

In an infinite geometric series, the terms in the sequence will get larger and larger closer to infinity if the common ration is greater than 1. Therefore, finding the sum of this series won’t get you a final answer.

But if the common ratio is -1< r < 1, and r is not equal to zero, as 0/0 is indeterminate. A final answer can be deduced by a formula:

Divergent and Convergent

Divergent – its series will increase indefinitely as more of its terms are added.

Convergent- its series will a definite limit as more of its terms are added.

In an infinite geometric series, the series will converge if the common ratio is -1 < r < 1 as the sum of its series is approaching a definite answer. The series will diverge if the common ration is greater than 1 so that the sum of the series will reach an answer of infinity.

Real life applications of Sequences and Series

For Example, the bacteria will multiply by 100 per minute, therefore there will be a sequence of containing the formula of 100^n when its growth starts from a population of 100.

Inquirers

I am an inquirer in doing this Ejournal as I am filled with curiosity that triggers me into finding all of the information above. due to this Ejournal, I am able to learn about the series topic into my brain and apply it into our daily lives and sustain my learning throughout life.