Question

$\displaystyle \sf\int_{0}^{ \infty } \frac{x^{2020} }{1 + x + {x}^{2} + \cdot\cdot\cdot \cdot\cdot\cdot + {x}^{2020} } \: dx$​​

Answer 1

Answer:

Integral doesn't converge

Step-by-step explanation:

$\displaystyle \sf\lim_{x \to \infty } \frac{ {x}^{2020} }{1 + x + {x}^{2}. \: . + {x}^{2020} } \\ \\ = \displaystyle \sf\lim_{x \to \infty } \frac{1}{ \frac{1}{ {x}^{2020} + }{\frac{1}{x {}^{2019} } } \: \: . \: . \: . \: .\: \: 1} \\ \\ = 1 \neq \: 0$

Answer 2

$\small\bold\red{Integral \: does \: not \: converge}$

• Please see attached file.

$\small\green{Thank \: You}$