1 + 2 + 3 + 4 + ⋯
Divergent series
Why this is trending
Interest in “1 + 2 + 3 + 4 + ⋯” spiked on Wikipedia on 2026-07-22.
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Key Takeaways
- The infinite series whose terms are the positive integers 1 + 2 + 3 + 4 + ⋯ is a divergent series.
- Because the sequence of partial sums fails to converge to a finite limit, the series does not have a sum.
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Source summary
WikipediaThe infinite series whose terms are the positive integers 1 + 2 + 3 + 4 + ⋯ is a divergent series. The nth partial sum of the series is the triangular number
which increases without bound as n goes to infinity. Because the sequence of partial sums fails to converge to a finite limit, the series does not have a sum.
While the series itself diverges to infinity, in certain mathematical contexts it can be assigned a finite value. In particular, the methods of zeta function regularization and Ramanujan summation assign the series a value of −+1/12, which is expressed by the famous formula
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