Question

[Huỳnh Thị Minh Hằng]

a) Tí​nh: [(1/2)-1].[(1/3)-1].[(1/4)-1]......[(1/100)-1]

​b) Tìm a(a€R): [1-(1/2)].[1-(1/3)].[1-(1/4)]....[1-(1/a+1)] = 1​​

Answer 1

[Akai Haruma]

Lời giải:

a.

$(\frac{1}{2}-1)(\frac{1}{3}-1)(\frac{1}{4}-1).....(\frac{1}{100}-1)$

$=\frac{-1}{2}.\frac{-2}{3}.\frac{-3}{4}....\frac{-99}{100}$

$=\frac{(-1)(-2)(-3)...(-99)}{2.3.4...100}$

$=\frac{-(1.2.3...99)}{2.3.4...100}=\frac{-1}{100}$

b.

$(1-\frac{1}{2})(1-\frac{1}{3})(1-\frac{1}{4})....(1-\frac{1}{a+1})=1$

$\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{a}{a+1}=1$

$\frac{1.2.3....a}{2.3.4...(a+1)}=1$

$\frac{1}{a+1}=1$

$\Rightarrow a+1=1\Rightarrow a=0$