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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