We can rewrite the product of these 31 fractions as a single expression using factorials:
Notice that the numerator is the factorial of 32, but missing the first term (
P=32!3231cap P equals the fraction with numerator 32 exclamation mark and denominator 32 to the 31st power end-fraction 3. Calculate the value Using the values for 323132 to the 31st power
P=2.6313×10351.2298×1048≈2.1396×10-13cap P equals the fraction with numerator 2.6313 cross 10 to the 35th power and denominator 1.2298 cross 10 to the 48th power end-fraction is approximately equal to 2.1396 cross 10 to the negative 13 power 4. Provide visual representation
The following graph shows how the cumulative product decreases as more terms are added to the sequence. The product of the sequence is exactly
To "prepare paper" for the expression , we must first define the product's range and then calculate its value. Assuming the sequence continues until the numerator reaches the denominator's value ( ), the product is:
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