Question

Resolução fatorial de 40!-39!/41!

Answer 1

• Resolvendo $\dfrac{40! - 39!}{41!}$:

Note que $\dfrac{40! - 39!}{41!} = \dfrac{40!}{41!} - \dfrac{39!}{41!}$.

Como $41! = 41 \cdot 40!$ e $41! = 41 \cdot 40 \cdot 39!$, então:

$\dfrac{40!}{41!} - \dfrac{39!}{41!} = \dfrac{40!}{41 \cdot 40!} - \dfrac{39!}{41 \cdot 40 \cdot 39!} \\\\\dfrac{40!}{41!} - \dfrac{39!}{41!} = \dfrac{1}{41} - \dfrac{1}{41 \cdot 40} = \dfrac{1}{41} - \dfrac{1}{1\,640}$

Como $1640 = 40 \cdot 41$, então:

$\dfrac{1}{41} - \dfrac{1}{1\,640} = \dfrac{40}{41 \cdot 40} - \dfrac{1}{1\,640} \\\\\dfrac{1}{41} - \dfrac{1}{1\,640} = \dfrac{40}{1\,640} - \dfrac{1}{1\,640} = \dfrac{39}{1\,640} \approx 0.0237$

Answer 2

Resposta:

40-39/41 = 40×39-39/41×40×39=

39(40-1)/41×40×39 = 40-1/41×40=

= 39/1640