Question

[(1/2)^-1 /(1/4)^-1] * (5/2)^-3​

Answer 1

Answer:

(1–1/2)=1/2

(1–1/2)(1–1/3)=1/2×2/3=1/3

(1–1/2)(1–1/3)(1–1/4)=1/2×2/3×3/4=1/3×3/4=1/4

(1–1/2)(1–1/3)(1–1/4)(1–1/5)=1/2×2/3×3/4×4/5=1/4×4/5=1/5

As you can see, the denominator of each term cancels out the numerator of the next term, so this series can be generalised to:

(1–1/2)(1–1/3)(1–1/4)…(1–1/n)=1/n

Which can also be written as:

1/2×2/3×3/4×…×((n-1)/n)=1/n

Answer 2

Answer:

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Step-by-step explanation:

[(1/2)^-1 ÷(1/4)^-1]* (5/2)^-3

(2÷4)×2/5^3

2×1/4×2/5×2/5×2/5

1/2×2/5×2/5×2/5

4/125 is the answer.

(hope this is correct )