another type of common series in analysis is the arithmetic series any such series can be evaluated from the basic formulan ii= ( for instanceto find the sum ( )rewrite it as ( ( )which is clearly ( )/ another way to remember this is to add the first and last terms (total )the second and next-to-last terms (total )and so on since there are / of these pairsthe total sum is ( )/ which is the same answer as before the next two formulas pop up now and then but are fairly uncommon = ( )( ik nk+ | = - when - the latter formula is not valid we then need the following formulawhich is used far more in computer science than in other mathematical disciplines the numbers hn are known as the harmonic numbersand the sum is known as harmonic sum the error in the following approximation tends to which is known as euler' constant hn = loge these two formulas are just general algebraic manipulationsn (nnf(ni= (ii= = (in - (ii= modular arithmetic we say that is congruent to modulo nwritten (mod )if divides intuitivelythis means that the remainder is the same when either or is divided by thus (mod as with equalityif (mod )then (mod nand ad bd (mod