<P> Although the series seems at first sight not to have any meaningful value at all , it can be manipulated to yield a number of mathematically interesting results , some of which have applications in other fields such as complex analysis , quantum field theory , and string theory . Many summation methods are used in mathematics to assign numerical values even to a divergent series . In particular , the methods of zeta function regularization and Ramanujan summation assign the series a value of − 1 / 12 , which is expressed by a famous formula : </P>
<P> Although the series seems at first sight not to have any meaningful value at all , it can be manipulated to yield a number of mathematically interesting results , some of which have applications in other fields such as complex analysis , quantum field theory , and string theory . Many summation methods are used in mathematics to assign numerical values even to a divergent series . In particular , the methods of zeta function regularization and Ramanujan summation assign the series a value of − 1 / 12 , which is expressed by a famous formula : </P>
what is the sum of all real numbers
what is the sum of all real numbers
− 1 / 12
− 1 / 12