Question

The simplified value of (1-1/3)(1-1/4)(1-1/5)......(1-1/99)
a)1/50 b) 2/99 c) 1/25 d) 1/100

Answer 1

Answer:

(b) 2/99

Step-by-step explanation:

(1-1/3)(1-1/4)(1-1/5)......(1-1/99)

= 2/3 × 3/4 × 4/5 ×...× 98/99

Notice that each denominator cancels with the following numerator, so the expression becomes:

= 2 / 99

Answer 2

The value of $(1-\dfrac{1}{3})(1-\dfrac{1}{4})(1-\dfrac{1}{5})......(1-\dfrac{1}{99})$ is "option b) $\dfrac{2}{99}$".

Step-by-step explanation:

We have,

$(1-\dfrac{1}{3})(1-\dfrac{1}{4})(1-\dfrac{1}{5})......(1-\dfrac{1}{99})$

To find, the vaue of $(1-\dfrac{1}{3})(1-\dfrac{1}{4})(1-\dfrac{1}{5})......(1-\dfrac{1}{99})=?$

∴ $(1-\dfrac{1}{3})(1-\dfrac{4}{5})(1-\dfrac{1}{5})......(1-\dfrac{1}{99})$

$=(\dfrac{3-1}{3})(\dfrac{4-1}{4})(\dfrac{5-1}{5})......(\dfrac{99-1}{99})$

$=(\dfrac{2}{3})(\dfrac{3}{4})(\dfrac{4}{5})......(\dfrac{99}{99})$

$=\dfrac{2}{3}\times\dfrac{3}{4}\times\dfrac{4}{5}......\times\dfrac{98}{99}$

$=\dfrac{2}{1}\times\dfrac{1}{1}\times\dfrac{1}{1}......\times\dfrac{1}{99}$

$=\dfrac{2}{99}$

The vaue of $(1-\dfrac{1}{3})(1-\dfrac{1}{4})(1-\dfrac{1}{5})......(1-\dfrac{1}{99})=\dfrac{2}{99}$

Hence, the value of $(1-\dfrac{1}{3})(1-\dfrac{1}{4})(1-\dfrac{1}{5})......(1-\dfrac{1}{99})$ is option b) $\dfrac{2}{99}$.