Find the value of the given expression:

Concept: For consecutive integers, each factor of the form (1 - 1/k) simplifies to (k-1)/k. When such factors are multiplied for consecutive values of k, the product telescopes: starting from the second factor onward, every numerator matches the denominator of the immediately preceding factor and cancels against it, so only the first factor's numerator (which has no preceding denominator to cancel against) and the very last factor's denominator (which has no following numerator to cancel against) survive.

1. Rewrite each bracket as a single fraction: (1 - 1/5) = 4/5, (1 - 1/6) = 5/6, (1 - 1/7) = 6/7, ... , (1 - 1/100) = 99/100.

2. Write the full product in order: (4/5) × (5/6) × (6/7) × ... × (99/100).

3. Cancel each numerator (from the second factor onward) with the denominator immediately before it: 5 cancels with 5, 6 cancels with 6, and this pattern continues all the way through 99.

4. After all the cancellation, only the first factor's numerator, 4, and the last factor's denominator, 100, remain, giving 4/100.

5. Simplify 4/100 by dividing numerator and denominator by 4 to get 1/25.

Cross-check: Apply the same rule to a short version of the pattern: (1 - 1/3)(1 - 1/4) = (2/3) × (3/4). Here the 3s cancel, leaving 2/4 = 1/2, exactly (first numerator)/(last denominator). The same telescoping logic on the full chain from 5 through 100 confirms the result 4/100 = 1/25.

So the value of the expression is 1/25.