## Sum Manipulation Methods

In practicing arithmetics, there are often situations, in which we want to manipulate sums in order to simplify them or to change their form into another that closer to some goal. The goal might be to prove something or to estimate the magnitude of the sum. This chapter is dedicated to some basic methods of sum manipulation.

| | | | created: 2015-02-19 20:56:24 | modified: 2019-01-20 22:12:46 | by: *bookofproofs*

## 1.**Definition**: Sums

## 2.**Proposition**: Basic Rules of Manipulating Finite Sums

## 3.**Proposition**: Product of Two Sums (Generalized Distributivity Rule)

## 4.**Proposition**: Double Summation

## 5.**Proposition**: Rule of Combining Different Sets of Indices

## 6.**Proposition**: The General Perturbation Method

## 7.Closed Formulas for Sums

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