1 on 1

In mathematics, 1 + 1 + 1 + 1 + ⋯, also written ⁠





∑

n
=
1


∞



n

0





{\displaystyle \textstyle \sum _{n=1}^{\infty }n^{0}}

⁠, ⁠





∑

n
=
1


∞



1

n





{\displaystyle \textstyle \sum _{n=1}^{\infty }1^{n}}

⁠, or simply ⁠





∑

n
=
1


∞


1



{\displaystyle \textstyle \sum _{n=1}^{\infty }1}

⁠, is a divergent series. Nevertheless, it is sometimes imputed to have a value of ⁠



−



1
2





{\displaystyle -{\tfrac {1}{2}}}

⁠, especially in physics. This value can be justified by certain mathematical methods for obtaining values from divergent series, including zeta function regularization.

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