COMEDK · Maths · 7. Binomial Theorem
\(\left(2^{3 n}-1\right)\) is divisible by
- A 6
- B 7
- C 8
- D 9
Answer & Solution
Correct Answer
(B) 7
Step-by-step Solution
Detailed explanation
The expression is \(2^{3n} - 1\). We can rewrite \(2^{3n}\) as \((2^3)^n\). Since \(2^3 = 8\), the expression becomes \(8^n - 1\). Using the algebraic identity \(x^n - 1 = (x - 1)(x^{n-1} + x^{n-2} + \dots + 1)\), we substitute \(x = 8\).…
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