Question
Download Solution PDFFind x if \(\frac{1}{{5!}} + \frac{1}{{6!}} = \frac{x}{{7!}}\) ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
n! = n × (n - 1) × ...... × 1
CALCULATION:
Given: \(\frac{1}{{5!}} + \frac{1}{{6!}} = \frac{x}{{7!}}\)
As we know that, n! = n × (n - 1) × ...... × 1
⇒ \(\frac{1}{{5!}} + \frac{1}{{6\; \times \;5!}} = \frac{x}{{7 \;\times \;6 \;\times \;5!}}\)
⇒ \(\frac{1}{{5!}} \times \left( {1 + \frac{1}{{6}}} \right) = \frac{1}{{5!}} \times \frac{x}{{42}}\)
⇒ \(1 + \frac{1}{{6}} = \frac{x}{{42}}\)
⇒ x = 49
Hence, option C is the correct answer.
Last updated on May 31, 2025
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