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By the principle of mathematical inducti...

By the principle of mathematical induction prove that for all natural number 'n' the following statement are true :
`(a) 2+4+6+........ +2n =n (n+1)`
`(b) 1+4+7+.......+(3n-2) =1/2 n (3n-1)`
`(C) 1^(3)+2^(3)+3^(3) +..........+n^(3)=1/4 n^(2)(n+1)^(2)`
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NAGEEN PRAKASHAN ENGLISH-PRINCIPLE OF MATHEMATICAL INDUCTION-Exercise 4
  1. By the principle of mathematical induction prove that for all natural ...

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  2. By the principle of mathematical induction prove that for every n in N...

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  3. By the principle of mathematical induction prove that for all natural ...

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  4. By the principle of mathematical induction prove that the following st...

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  5. By the principle of mathematical induction prove that the following s...

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  6. Prove the following by the principle of mathematical induction:\ 2....

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  7. Prove by induction that the sum Sn=n^3+3n^2+5n+3 is divisible by 3 for...

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  8. " if " a^(1) =a,a^(r+1) =a^(r).a " prove that :" (ab)^(n) =a^(n)b^(n...

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  9. By the principle of mathematical induction prove that 3^(2^(n))-1, is ...

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  10. Prove the following by the principle of mathematical induction:\ 7^...

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  11. Prove the following by the principle of mathematical induction: 7+7...

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

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

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

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  15. 1+1/(1+2)+1/(1+2+3)+1/(1+2+3+n)=(2n)/(n+1)

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  16. Using the principle of mathematical induction, prove that : 1. 2. 3+2...

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  17. Using the principle of mathematical induction, prove that : 1. 2. 3+2...

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  18. 1.3+2.3^2+3.3^3+..............+n.3^n=((2n-1)3^(n+1)+3)/4

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  19. 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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  20. 1.3+3.5+5.7+......+(2n-1)(2n+1)=(n(4n^2+6n-1))/3

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