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Consider the statement ''p(n):9^n-1 is a...

Consider the statement ''`p(n):9^n-1` is a multiple of 8''. Where n is a natural number.
Assuming `p(k)` is true, show that `p(k+1)` is true.

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MAXIMUM PUBLICATION-PRINCIPLE OF MATHEMATICAL INDUCTION-EXAMPLE
  1. For all nge1, prove that p(n):2.7^n+3.5^n-5 is divisible by 24.

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  2. Consider the statement ''p(n):9^n-1 is a multiple of 8''. Where n is a...

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  3. Consider the statement ''p(n):9^n-1 is a multiple of 8''. Where n is a...

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  4. Consider the statement ''P(n):x^n-y^n is divisible by x-y''. Show th...

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  5. Consider the statement ''P(n):x^n-y^n is divisible by x-y''. Using t...

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  6. Consider the statement ''7^n-3^n is divisible by 4'' Verify the resu...

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  7. Consider the statement ''7^n-3^n is divisible by 4'' Prove the state...

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  8. Which among the following is the least number that will divide 7^(2n)-...

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  9. Prove by mathematical induction. (costheta +i sintheta)^n=(cosntheta...

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  10. Given P(n):3^(2n) -1 is divisible by 8 Check whether P(1) is true...

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  11. Given P(n):3^(2n) -1 is divisible by 8. If P(k) is true then prove P...

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  12. Given P(n):3^(2n) 1 is divisible by 8. Is the statement P(n) true f...

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  13. Prove that by 1.2+2.3+3.4+…..+n(n+1)=(n(n+1)(n+2))/3 by using the prin...

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  14. By the Principal of mathematical induction, prove that 1+5+5^2+…..+5^(...

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  15. Consider the statement P(n):n(n+1)(2n+1) is divisible by 6. Verify t...

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  16. Consider the statement P(n):n(n+1)(2n+1) is divisible by 6. By assum...

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  17. Consider the statement P(n):1^2+2^2+3^2+…….+n^2=(n(n+1)(2n+1))/6 C...

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  18. Consider the statement P(n):1^2+2^2+3^2+…….+n^2-(n(n+1)(2n+1))/6 B...

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  19. Consider the statement P(n):1^2+2^2+3^2+…….+n^2=(n(n+1)(2n+1))/6 I...

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  20. Consider the statement P(n)=1+3+3^2+…….+3^(n-1)=frac(3^(n-1))(2) C...

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