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If P(n) is the statement n^3+n is divisi...

If `P(n)` is the statement `n^3+n` is divisible by 3, prove that `P(3)` is true but `P(4)` is not true.

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RD SHARMA ENGLISH-MATHEMATICAL INDUCTION-All Questions
  1. Let P(n) be the statement 7 divides (2^(3n)-1)dot What is P(n+1)?

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  2. If P(n) is the statement n(n+1) is even, then what is P(3)?

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  3. If P(n) is the statement n^3+n is divisible by 3, prove that P(3) is t...

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  4. If P(n) is the statement n^2+n is even, and if P(r) is true then P(r+1...

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  5. If P(n) is the statement 2^ngeq3n , and if P(r) is true, prove that P(...

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  6. Given an example of a statement P(n) such that it is true of all n ϵN.

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  7. If P(n) is the statement n^2-n+41 is prime. Prove that P(1),\ P(2)a n ...

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  8. Given an example of a statement P(n) which is true for all ngeq4 but P...

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  9. Prove by the principle of mathematical induction that for all n in N...

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  10. Using principle of mathematical induction prove that x^(2n)-y^(2n) i...

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

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  12. Prove by induction that 4+8+12++4n=2n(n+1) for all n Ndot

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  13. prove that cosalpha\ cos2alpha\ cos4alpha......cos(2^(n-1)alpha)=(si...

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  14. Let U1=1,\ U2=1\ a n d\ U(n+2)=U(n+1)+Un for\ngeq1. use mathematical i...

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  15. Prove the following by the principle of mathematical induction: 1+2...

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  16. Prove the following by the principle of mathematical induction: 1^2...

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

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  18. Using the principle of mathematical induction, prove that 1/(1*2)...

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

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  20. Prove the following by the principle of mathematical induction:1/(2...

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