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Observe the following pattern of dots ...

Observe the following pattern of dots

i) Find the number of dots in the `n^(th)` pattern.
ii) Find the sum of number of dots upto `n^(th)` pattern and the mathematical statement using these facts.
iii)Prove the statement obtained in question (ii) using principle of mathematical induction.

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V PUBLICATION-PRINCIPLE OF MATHEMATICAL INDUCTION-QUESTION BANK
  1. Using mathematical induction prove that 1/(1.4)+1/(4.7)+1/(7.10)+......

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

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

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

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

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

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

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

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

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

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  11. Observe the following pattern of dots i) Find the number of dots i...

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  12. If P(n) is the statement n(n+1) is even then what about P(6)?

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  13. If P(n) is the statement n(n+1)(n+2) is divisiblé by 12, prove that P...

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

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  15. Prove 'that 10^n+3 xx 4^(n+2)+5 is divisible by 9 .

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

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  17. Prove that 1(1) !+2(2) !+3(3) !+............ .+n(n) ! = (n+1) !-1

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  18. Prove that 1+(1)/(4)+(1)/(9)+...........+(1)/(n^(2))lt2-(1)/n,(ngt1)

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  19. Using principle of mathematical induction, prove that the product of t...

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

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