(2/48)(3/48)(4/48)(5/48)(6/48)(7/48)(8/48)(9/48... Apr 2026

This sequence is a perfect illustration of or exponential decay. In statistics, if you were looking for the probability of 47 independent events occurring—where each event has a progressively higher but still limited chance of success—the likelihood of the entire chain succeeding is almost non-existent.

The graph above shows the "collapse" on a logarithmic scale. Even as the individual terms (like 47/48) approach 1, they are unable to reverse the momentum of the tiny fractions at the start of the chain. (2/48)(3/48)(4/48)(5/48)(6/48)(7/48)(8/48)(9/48...

In this structure, the numerator is the product of all integers from 1 to 48 (though the sequence starts at 2, This sequence is a perfect illustration of or

doesn't change the value). The denominator is 48 multiplied by itself 47 times. Because the denominator grows exponentially while the numerator grows factorially, the denominator quickly overwhelms the top of the fraction. The Result The final value of this calculation is approximately . To put that into perspective: Decimal form: 0.00000000000000000119 Even as the individual terms (like 47/48) approach

AI responses may include mistakes. For legal advice, consult a professional. Learn more

This is roughly equivalent to one second compared to 26 billion years. Why It Matters

48!4847the fraction with numerator 48 exclamation mark and denominator 48 to the 47th power end-fraction