AP EAMCET · Maths · Mathematical Induction
Let \(P(n): 2+2^2+2^3+\ldots+2^n=2^{n+1}, n \in \mathbf{N}\). Then,
- A \(P(m)\) is true \(\Rightarrow P(m+1)\) is true
- B \(P(n)\) is true for all \(n \in \mathrm{N}\)
- C \(P(n)\) is true for all \(n \geq 20\)
- D \(P(n)\) is true for all \(n \leq 10\)
Answer & Solution
Correct Answer
(A) \(P(m)\) is true \(\Rightarrow P(m+1)\) is true
Step-by-step Solution
Detailed explanation
Given, \(p(n)=2+2^2+2^3+\ldots .+2^n=2^{n+1}\) Where \(n \in \mathrm{N}\). Let \(p(m)\) is true then, \(P(m)=2+2^2+2^3+\ldots .+2^m=2^{m+1}\) So,…
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