Question 16
The fraction $$\frac{(2 \times 3 \times 4)+(4 \times 6 \times 8)+(6 \times 9 \times 12)+\cdots+(20 \times 30 \times 40)}{(1 \times 2 \times 3)+(2 \times 4 \times 6)+(3 \times 6 \times 9)+\cdots+(10 \times 20 \times 30)}$$ reduces to
Correct Answer: 4
Solution
The $$k$$th term in the numerator is $$(2k)(3k)(4k)=24k^3$$. The corresponding denominator term is $$k(2k)(3k)=6k^3$$. Every numerator term is therefore four times its matching denominator term, so the complete fraction equals $$4$$.
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