Question

o Produto (1-1/2) . (1-1/3) . (1-1/4) . (1-1/5) .... (1-1/2020) é igual a:

Answer 1

A questão pede o seguinte produto:

$P = \left(1-\dfrac{1}{2}\right) \left(1-\dfrac{1}{3}\right) \left(1-\dfrac{1}{4}\right)\cdot\cdots\cdot\left(1-\dfrac{1}{2019}\right)\cdot \left(1-\dfrac{1}{2020}\right)$

$P = \left(\dfrac{2}{2}-\dfrac{1}{2}\right) \left(\dfrac{3}{3}-\dfrac{1}{3}\right) \left(\dfrac{4}{4}-\dfrac{1}{4}\right)\cdot\cdots\cdot\left(\dfrac{2019}{2019}-\dfrac{1}{2019}\right)\cdot \left(\dfrac{2020}{2020}-\dfrac{1}{2020}\right)$

$P = \left(\dfrac{1}{2}\right) \left(\dfrac{2}{3}\right) \left(\dfrac{3}{4}\right)\cdot\cdots\cdot\left(\dfrac{2018}{2019}\right)\cdot \left(\dfrac{2019}{2020}\right)$

Fazendo o famoso corta corta:

$P = \dfrac{1}{2020}$

Answer 2

Resposta:

Explicação passo-a-passo:

Ele ta certin