diff --git a/guide/english/book-recommendations/index.md b/guide/english/book-recommendations/index.md index 234608c2f8..ca029e103b 100644 --- a/guide/english/book-recommendations/index.md +++ b/guide/english/book-recommendations/index.md @@ -371,6 +371,13 @@ title: Books to Read for Programmers - http://javascriptbook.com/ - ISBN-13: 978-1118531648 +# Design Patterns + +https://www.amazon.com/Design-Patterns-Elements-Reusable-Object-Oriented/dp/0201633612/ + +https://www.amazon.com/Head-First-Design-Patterns-Brain-Friendly/dp/0596007124 + + This list was compiled from multiple suggestion threads on Reddit and Stackoverflow. Please feel free to add more that you have found useful! diff --git a/guide/english/mathematics/geometric-series/index.md b/guide/english/mathematics/geometric-series/index.md index 8c0afe3f23..f2209395ef 100644 --- a/guide/english/mathematics/geometric-series/index.md +++ b/guide/english/mathematics/geometric-series/index.md @@ -3,13 +3,42 @@ title: Geometric Series --- ## Geometric Series -This is a stub. Help our community expand it. -This quick style guide will help ensure your pull request gets accepted. +A geometric progression is a sequence of numbers, whose first term is non zero and each term is obtained by multiplying its proceding term by a constant quantity. This constant quantity is called common ratio of the GP. - +The sum of this progression is called geometric series. -#### More Information: - +We can say if a1,a2,a3,....,an are in GP then + + is known as common ratio of GP. + + if a is the first term then GP can be written as + +example of a GP : 2,4,8,16,.... + +## The nth term of GP (Also known as General term) + +Let a be the first term, r be the common ratio and l be the last term of a GP, then nth term is given by + + + + where + + # The sum of n terms of a GP + + Let a be the first term, r be the common ratio and l be the last term of a GP, then sum of n terms is given by: + + + and is not defined for r=1 + +# Geometric Mean + +if we insert geometric mean between two numbers and , then + +Geometric mean = + + + +