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Prove that 2^n > nfor all positive inte...

Prove that `2^n > n`for all positive integers n.

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To prove that \( 2^n > n \) for all positive integers \( n \) using the Principle of Mathematical Induction, we will follow these steps: ### Step 1: Base Case We start by checking the base case, which is \( n = 1 \). \[ 2^1 = 2 > 1 \] ...
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NCERT ENGLISH-PRINCIPLE OF MATHEMATICAL INDUCTION-EXERCISE 4.1
  1. Prove that 2^n > nfor all positive integers n.

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  2. Prove the following by using the principle of mathematical induction ...

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  3. Prove the following by using the principle of mathematical induction ...

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  4. Prove the following by using the principle of mathematical induction ...

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  5. Prove the following by using the principle of mathematical induction ...

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  6. Prove the following by using the principle of mathematical induction ...

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  7. Prove the following by the principle of mathematical induction: 1/(1...

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  8. Prove by the principal of mathematcal induction that for all n in N. ...

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  9. Prove the following by using the principle of mathematical induction ...

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  10. Prove the following by the principle of mathematical induction:\ n(...

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  11. Prove the following by using the principle of mathematical induction ...

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  12. Prove the following by using the principle of mathematical inductio...

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  13. Prove the following by using the principle of mathematical induction ...

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  14. Prove the following by using the principle of mathematical induction ...

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  15. Prove by the principle of induction that for all n N ,\ (10^(2n-1)+1)...

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  16. Prove the following by using the principle of mathematical induction ...

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  17. Prove the following by the principle of mathematical induction: 1+3...

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  18. Prove the following by using the principle of mathematical induction ...

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  19. Using the principle of mathematical induction, prove that 1+1/(1+2)+...

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  20. Prove the following by using the principle of mathematical induction ...

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  21. Using the principle of mathematical induction prove that : 1. 3+2. 3^...

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