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For every positive integer n,prove that `7^n-3^n` is divisible by 4 using principle of mathematical induction.

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V PUBLICATION-PRINCIPLE OF MATHEMATICAL INDUCTION-QUESTION BANK
  1. Prove that 2^n gt n for all positive integtrs n.

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  2. For all nge1, prove that 1/1.2+1/2.3+1/3.4+..........+1/(n(n+1))=n/(...

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  3. For every positive integer n,prove that 7^n-3^n is divisible by 4 usin...

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  4. Prove that (1+x)^n ge1+n x, for all natural number 'n', where x gt-1.

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  5. For all nge1, prove that p(n):2.7^n+3.5^n-5 is divisible by 24.

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  6. For all nge1, prove that 1^2+2^2+3^2+……….+n^2gtn^3/3

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  7. Prove that the rule of exponents (a b)^n=a^n b^n by using principle of...

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  8. Prove by using the principal of Mathematical Induction P(n)=1+3+3^2+…....

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  9. Using mathematical induction prove that 1^3+2^3+3^3+.....+n^3=[(n(n+1)...

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  10. For all nge1, prove that 1+1/((1+2))+1/((1+2+3))+.......+1/((1+2+3+....

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  11. For all nge1, prove that 1.2.3+2.3.4+......+n(n+1)(n+2)=(n(n+1)(n+2)(n...

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  12. Using mathematical induction prove 1cdot3+2cdot3^2+3cdot3^3+.....+ncdo...

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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. Using mathematical induction prove that 1cdot3+3cdot5+5cdot7+.....+(...

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  15. Using mathematical induction prove that 1cdot2+2cdot2^2+......+ncdot...

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  16. A statement p(n) for a natural number n is given by p(n):1/2+1/4+1/8...

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  17. Using mathimatical induction prove that 1/(2.5)+1/(5.8)+1/(8.11)+......

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  18. Using mathematical induction prove that 1/(1.2.3)+1/(2.3.4)+......+1...

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  19. Consider the following statement: P(n):a+ar+ar^2+……+ar^(n-1)=(a(r^n-...

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  20. Using mathematical induction prove that (1+3/1)(1+5/4)(1+7/9)......(...

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