Question

Calculaţi:

1 1/2 x 1 1/3 x 1 1/4 x 1 1/5 x ..... x 1 1/1000

Answer 1

Răspuns

$\dfrac{1001}{2}$

Explicație pas cu pas:

$1\dfrac{1}{2}\cdot1\dfrac{1}{3}\cdot 1\dfrac{1}{4}\cdot 1\dfrac{1}{5}\cdot \ldots\cdot 1\dfrac{1}{1000}=\dfrac{2+1}{2}\cdot \dfrac{3+1}{3}\cdot \dfrac{4+1}{4}\cdot\ldots \cdot \dfrac{1000+1}{1000}=\\=\dfrac{3}{2}\cdot \dfrac{4}{3}\cdot \dfrac{5}{4}\cdot \ldots\cdot \dfrac{1001}{1000}=\bold{\dfrac{1001}{2}}$