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Printjmc
algebra intermediate
Problem
What is the value of if ?
Solution
The numerator is equal to . The exponent is the sum of the first 9 consecutive positive integers, so its sum is . So the numerator is .
The denominator is equal to . The exponent is twice the sum of the first 6 consecutive positive integers, so its sum is . So the denominator is .
The entire fraction becomes . Plugging in yields .
The denominator is equal to . The exponent is twice the sum of the first 6 consecutive positive integers, so its sum is . So the denominator is .
The entire fraction becomes . Plugging in yields .
Final answer
125