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Consider the following statement: P(n)...

Consider the following statement:
`P(n):a+ar+ar^2+……+ar^(n-1)=(a(r^n-1))/(r-1)`
Hence by using the principle of mathematical induction, prove that `P(n)` is true for all natural numbers `n`.

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A N EXCEL PUBLICATION-PRINCIPLE OF MATHEMATICL INDUCTION-QUESTION BANK
  1. Using mathimatical induction prove that 1/(2.5)+1/(5.8)+1/(8.11)+......

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

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

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

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  5. Using mathematical induction prove that (1+1/1)(1+1/2)(1+1/3)......(...

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  6. Using mathematical induction prove that 1^2+3^2+5^2+.....+(2n-1)^2=(...

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  7. Using mathematical induction prove that 1/(1.4)+1/(4.7)+1/(7.10)+......

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  8. Using mathematical induction prove that 1/(3.5)+1/(5.7)+1/(7.9)+.......

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  9. For all nge1,prove that 1+2+3+……+nlt1/8(2n+1)^2

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  10. Using principle of mathematical induction prove that n(n+1)(n+5) is a ...

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  11. Using mathematical induction prove that 10^(2n-1)+1 is divisible by 1...

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  12. Using mathematical induction prove that x^(2n)-y^(2n) is divisible by ...

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  13. Consider the statement P(n)=3^(2n+2)-8n-9 is divisible by 8 Prove ...

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  14. Using mathematical induction prove that 41^n-14^n is a multiple of 2...

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  15. Using mathematical induction prove that (2n+7) lt (n+3)^2 for all n in...

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  16. Consider the statement P(n):2^(3n) -1 is divisible by 7 Is the state...

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  17. Consider the statement P(n):2^(3n) -1 is divisible by 7 If p(k) is t...

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  18. Let P(n) be the statement "n+3" is prime. Is P(3) true? What is your...

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  19. Let P(n) denotes the statement 10^(2n-1)+1 is divisible by 11. If P(m)...

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

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