COMEDK · Maths · 6. Mathematical Induction
\(2^{3 n}-7 n-1 \text { is divisible by }\)
- A 64
- B 36
- C 49
- D 25
Answer & Solution
Correct Answer
(C) 49
Step-by-step Solution
Detailed explanation
Let \(f(n) = 2^{3n} - 7n - 1 = 8^n - 7n - 1\). Using the binomial expansion, \(8^n = (1 + 7)^n = 1 + ^{n}C_{1}(7) + ^{n}C_{2}(7^2) + ^{n}C_{3}(7^3) + \dots + ^{n}C_{n}(7^n)\). Substituting this into the expression for \(f(n)\):…
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