Question
Download Solution PDFWhat is the remainder when 7n - 6n is divided by 36 for n = 100?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Let p(n) = 7n – 6n
= (6+1)n – 6n
= 1+6n +nC262 + nC363+.......... 6n -6n)
= 1+ 62(nC2+ nC3 × 6 +....... 6n-2)
= 1+ 36(100C2 + 100C3 × 6 +........698).....(n =100)
= 1 + 36 k
where k = (100C2 + 100C3 × 6 +........698)
Thus When 7n – 6n is divided by 36, the remainder will be 1
∴ Option (b) is correct
Last updated on May 30, 2025
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