e-e-e-1-3-e-1-4-e-1-5-e-1-6-e-1-7-e-1-8-

Question Number 88360 by jagoll last updated on 10/Apr/20

\frac{e}{\sqrt{e}} \times \frac{\sqrt[3]{e}}{\sqrt[4]{e}} \times \frac{\sqrt[5]{e}}{\sqrt[6]{e}} \times \frac{\sqrt[7]{e}}{\sqrt[8]{e}} \times \dots = ?

Commented by john santu last updated on 10/Apr/20

= e^{1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \frac{1}{5} - \frac{1}{6} + \dots}

[\ln (1 + x) = x - \frac{x^{2}}{2} + \frac{x^{3}}{3} - \frac{x^{4}}{4} + \dots]

- 1 < x ⩽ 1, \ln (2) = 1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \dots]

\Rightarrow= e^{\ln (2)} = 2 .

Commented by jagoll last updated on 10/Apr/20

thank you

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