Question

Find the value of \((1-(\frac{1}{3}))(1-(\frac{1}{3}))(1-(\frac{1}{4}))(1-(\frac{1}{5}))....(1-(\frac{1}{100}))\)

• A. \(\frac{1}{25}\)
• B. \(\frac{1}{50}\)
• C. \(\frac{1}{15}\)
• D. \(\frac{1}{45}\)

Answer 1

The Correct Option is B

Step 1: The given expression is: 

\[ 1 - \frac{1}{3}, 1 - \frac{1}{4}, 1 - \frac{1}{5}, ... , 1 - \frac{1}{100} \]

Rewriting in fraction form:

\[ \frac{2}{3} \times \frac{3}{4} \times \frac{4}{5} \times ... \times \frac{99}{100} \]

Step 2: Most of the terms cancel out, leaving:

\[ \frac{2}{100} \]

Step 3: Simplifying the expression:

\[ \frac{2}{100} = \frac{1}{50} \]

Thus, the correct answer is: \(\frac{1}{50}\).