Question

61. Find the value of (1-(1/3))(1-(1/4))(1-(1/5))....(1-(1/100))
(A) 1/25
(B) 1/50
(C) 1/15
(D) 1/45​

Answer 1

Answer:

(2/3)*(3/4)*(4/5)*(5/6)*....(99/100)=2/100=1/50

Answer 2

Option (B) is correct.

Step-by-step explanation:

Since we have given that

$(1-\dfrac{1}{3})(1-\dfrac{1}{4})(1-\dfrac{1}{5})....................(1-\dfrac{1}{100})\\\\=\dfrac{2}{3}\times \dfrac{3}{4}\times \dfrac{4}{5}\times \dfrac{99}{100}\\\\=\dfrac{2}{100}\\\\=\dfrac{1}{50}$

Hence, Option (B) is correct.

# learn more:

Find the value of (2-1/3)(1-1/4)(1-1/5)......(1-1/99)(1-1/100)

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