Pk=∏n=2k+1n10cap P sub k equals product from n equals 2 to k plus 1 of n over 10 end-fraction 2. Evaluate the Limit As the product continues, you eventually reach terms where , the term is
, which does not change the product's value. However, for every term after , the fraction n10n over 10 end-fraction is greater than , which would typically cause a product to grow. (2/10)(3/10)(4/10)(5/10)(6/10)(7/10)(8/10)(9/10...
The plot below shows how the product's value drops rapidly as you multiply the first several terms. Final Result ✅The product reaches its lowest value of 0.00362880.0036288 Pk=∏n=2k+1n10cap P sub k equals product from n
from fractions import Fraction def calculate_sequence(n): result = Fraction(1, 1) for i in range(2, n + 1): result *= Fraction(i, 10) return float(result) # Check the first few values to see the trend sequence_values = {f"({i}/10)": calculate_sequence(i) for i in range(2, 11)} print(sequence_values) Use code with caution. Copied to clipboard The plot below shows how the product's value
The value of the infinite product is 1. Analyze the General Term The sequence consists of multiplying terms in the form n10n over 10 end-fraction starting from -th term of this product can be written as:
. If the sequence is part of a probability problem where terms must be ≤1is less than or equal to 1 , it effectively vanishes.