find-S-1-1-1-1-1-1-1-1-1-1-1-1-2-1-2-1-2-1-3-1-3-1-3-1-4-1-4-1-4-1-5-

Question Number 206393 by MaruMaru last updated on 13/Apr/24

find S = 1 + \sum_{ℓ} \frac{{(-)}^{ℓ}}{ℓ} (\frac{1}{ℓ} - \frac{1}{ℓ + 1}), ℓ \in [1, \infty)

1 + \sum_{ℓ} \frac{{(-)}^{ℓ}}{ℓ} (\frac{1}{ℓ} - \frac{1}{ℓ + 1})

1 - (1 - \frac{1}{2}) + \frac{1}{2} (\frac{1}{2} - \frac{1}{3}) - \frac{1}{3} (\frac{1}{3} - \frac{1}{4}) + \frac{1}{4} (\frac{1}{4} - \frac{1}{5}) - \dots \dots

Answered by MaruMaru last updated on 17/Apr/24

\dots .

Facebook Tweet Pin