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`1`		`-# 1.3. Reasoning about correctness`
	`1`	`+---`
	`2`	`+layout: post`
	`3`	`+category: algorithm-design-manual`
	`4`	`+title: 1.3. Reasoning about correctness`
	`5`	`+---`
`2`	`6`
`3`	`7`	`## An algorithm`
`4`	`8`
`@@ -52,15 +56,15 @@ the loop effects the base`
`52`	`56`
`53`	`57`	`* for p ≥ 1`
`54`	`58`
`55`		`-![image](https://raw.github.com/csabapalfi/algorithm-design-manual/master/arithmetic_progressions.jpg)`
	`59`	`+![image](images/arithmetic_progressions.jpg)`
`56`	`60`
`57`	`61`	`* p < -1, this sum always converges to a constant`
`58`	`62`
`59`	`63`	`### Geometric progressions`
`60`	`64`
`61`	`65`	`the loop effects the exponent`
`62`	`66`
`63`		`-![image](https://raw.github.com/csabapalfi/algorithm-design-manual/master/geometric_progressions.jpg)`
	`67`	`+![image](images/geometric_progressions.jpg)`
`64`	`68`
`65`	`69`	`interpretation depends upon the base of the progression`
`66`	`70`

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`1`		`-# 1.4 Modeling the Problem`
	`1`	`+---`
	`2`	`+layout: post`
	`3`	`+category: algorithm-design-manual`
	`4`	`+title: 1.4 Modeling the Problem`
	`5`	`+---`
`2`	`6`
`3`	`7`	`* modeling translates a real-world application into an abstract model which consists of procedures on fundamental structures`
`4`	`8`	`* a precisely described model allow you to re-use well-understood solutions from algorithms literature`
`@@ -23,7 +27,7 @@`
`23`	`27`
`24`	`28`	`## Recursive Objects`
`25`	`29`
`26`		`-Big things that are made from smaller things of exactly the same type as the big thing. A decomposition rule describes how to get smaller things from big things.`
	`30`	`+Big things that are made from smaller things of exactly the same type as the big thing. A decomposition rule describes how to get smaller things from big things.`
`27`	`31`
`28`	`32`	`As all combinatorial objects above are recursive objects here are a few possible decompositon rules for them:`
`29`	`33`

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