Question

$\sqrt(1-1/2)*(1-1/3)*(1-1/4)*.....*(1-1/36)=$
repede va rog

Answer 1

Răspuns:

1-1/2=1/2

1-1/3=2/3

1-1/4=3/4

.....................

1-1/35=34/35

1-1/36=35/36

√(1-1/2)(1-1/3)(1-1/4)·...·(1-1/35)(1-1/36)=

√1/2·2/3·3/4·...·34/35·35/36=se simplifica  numitorul primei fractii  cu numaratorul    urmatoarei  fractii  si  se   obtine

√1/36=1/6

Explicație pas cu pas:

Answer 2

$\sqrt{(1-\dfrac{1}{2})(1-\dfrac{1}{3})(1-\dfrac{1}{4})\cdot\ ...\ \cdot(1-\dfrac{1}{36})}=\sqrt{\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdoty\ ...\ \cdot\dfrac{35}{36}}=\sqrt{\dfrac{1}{36}}=\dfrac{1}{6}$