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Using binomial theorem, prove that 2^(3n...

Using binomial theorem, prove that `2^(3n)-7^n-1` is divisible by `49` , where `n in Ndot`

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NAGEEN PRAKASHAN-PRINCIPLE OF MATHEMATICAL INDUCTION-Exercise 4
  1. Prove the following by using the principle of mathematical induction ...

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  2. Using the principle of mathematical induction ,prove that (1+x)^ngeq(1...

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  3. Using binomial theorem, prove that 2^(3n)-7^n-1 is divisible by 49 , w...

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  4. 1+1/(1+2)+1/(1+2+3)+1/(1+2+3+n)=(2n)/(n+1)

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  5. If P(n)= 1. 2 .3+2. 3 .4+....+n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/4 then P...

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  6. 1. 2 .3+2. 3 .4++n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/4

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  7. 1.3+2.3^2+3.3^3+..............+n.3^n=((2n-1)3^(n+1)+3)/4

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  8. Prove by PMI that 1.2+ 2.3+3.4+....+ n(n+1) =((n)(n+1)(n+2))/3, AA n i...

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  9. 1.3+3.5+5.7+......+(2n-1)(2n+1)=(n(4n^2+6n-1))/3

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  10. 1.2+2.2^2+3.2^3+.....+n.2^n=(n-1)2^(n-1)+2

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  11. 1/2+1/4+1/8+1/16+.......+1/2^n=

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

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  13. Using the principle of mathematical induction prove that 1/(1. 2. ...

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  14. Prove the following by using the principle of mathematical induction ...

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  15. Prove the following by using the principle of mathematical induction ...

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  16. (1+(1)/1)(1+(1)/(2))(1+(1)/(3))......(1+(1)/n) n(n+1)

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  17. 1^(2)+3^(2)+5^(2)+.......+(2n-1)^(2) =(n(2n-1)(2n+1))/(3)

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

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

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  20. Prove that 1+2+3+4........+N<1/8(2n+1)^2

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