History of Grandi's series
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Geometry and infinite zeros — Grandi — Guido Grandi (1671–1742) reportedly provided a simplistic account of the

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Beginning of the published Leibniz-Wolff letter

Start of Positiones part 3, as reprinted in 1744

Image: Varignon Précautions

(1, 1⁄2) on the witch of Agnesi

Harmonic series (mathematics)
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In mathematics, the harmonic series is the divergent infinite series: — ∑

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Image: Harmonischebrueckerp

The first fourteen partial sums of the alternating harmonic series (black line segments) shown converging to the natural logarithm of 2 (red line).

1 + 2 + 3 + 4 + ⋯
[videos]
The infinite series whose terms are the natural numbers 1 + 2 + 3 + 4 + ⋯ is a divergent series. The nth partial sum of

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Passage from

Ramanujan's first notebook describing the "constant" of the series

The first six triangular numbers

1 − 2 + 3 − 4 + ⋯
[videos]
In mathematics, 1 − 2 + 3 − 4 + ··· is the infinite series whose terms are the successive positive integers, given

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Excerpt from p.233 of the E212 — Institutiones calculi differentialis cum eius usu in analysi finitorum ac doctrina serierum. Euler sums similar series, ca. 1755.

1 − 2 + 4 − 8 + ⋯
[videos]
In mathematics, 1 − 2 + 4 − 8 + ⋯ is the infinite series whose terms are the successive powers of two with alternating

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Excerpt from the Institutiones

1 + 1 + 1 + 1 + ⋯
[videos]
In mathematics, 1 + 1 + 1 + 1 + ⋯, also written — ∑ — n

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