Math Problem Statement
Solution
The problem involves evaluating the product:
Let's simplify each term in the product individually:
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Each term can be rewritten as:
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Therefore, the product becomes:
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Notice that this sequence has a telescoping effect, where most terms in the numerator and denominator will cancel each other out. Specifically:
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Therefore, the result of the entire product is:
The correct answer is (B) 5.
Would you like a further breakdown of telescoping products or have any questions on similar problems? Here are some additional questions that might expand your understanding:
- How does the telescoping property simplify complex products or sums?
- What other types of mathematical expressions benefit from telescoping?
- Could a similar technique apply to sums rather than products?
- How would this approach change if terms didn’t fully cancel?
- What other problems could be simplified using partial fraction decomposition?
Tip: When faced with a long sequence of fractions in a product, look for a telescoping pattern—it often simplifies calculations significantly!
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Math Problem Analysis
Mathematical Concepts
Algebra
Fractions
Telescoping Products
Formulas
1 + 1/n = (n + 1)/n
Theorems
Telescoping property of products
Suitable Grade Level
Grades 8-10
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