Question

What is the value of (1 - 1/2) × (1 - 1/3) × (1-1/4) ....... × (1 - 1/10) = ?

• A. 9/10
• B. 9
• C. 1/10
• D. 1/2

Answer 1

Answer:

C. 1/10

The value of the expression is $\frac{1}{10}$ (or 0.1).

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Step 1: Simplify each individual bracket

Convert each mixed subtraction into a single fraction ($1 - \frac{1}{n} = \frac{n-1}{n}$):

• $(1 - \frac{1}{2}) = \frac{1}{2}$

• $(1 - \frac{1}{3}) = \frac{2}{3}$

• $(1 - \frac{1}{4}) = \frac{3}{4}$

• ... up to $(1 - \frac{1}{10}) = \frac{9}{10}$

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Now, substitute the simplified fractions back into the equation:
$\frac{1}{2} \times \frac{2}{3} \times \frac{3}{4} \times \frac{4}{5} \times \dots \times \frac{8}{9} \times \frac{9}{10}$

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Step 3: Cancel common numbers

Notice how the denominator of each fraction perfectly cancels out the numerator of the very next fraction:
$\frac{1}{\cancel{2}} \times \frac{\cancel{2}}{\cancel{3}} \times \frac{\cancel{3}}{\cancel{4}} \times \dots \times \frac{\cancel{8}}{\cancel{9}} \times \frac{\cancel{9}}{10}$

After all cross-cancellations, only the first numerator (1) and the last denominator (10) will remain:
$\mathbf{\frac{1}{10}}$