Home
Class 11
MATHS
Prove by the principle of mathematical i...

Prove by the principle of mathematical induction that for all `n in N :` `1^2+2^2+3^2++n^2=1/6n(n+1)(2n+1)`

Promotional Banner

Topper's Solved these Questions

  • LINEAR INEQUATIONS

    RD SHARMA ENGLISH|Exercise All Questions|163 Videos

  • MATHEMATICAL REASONING

    RD SHARMA ENGLISH|Exercise All Questions|182 Videos

Similar Questions

Explore conceptually related problems

Prove by the principle of mathematical induction that n<2^n"for all"n in Ndot

Prove by the principle of mathematical induction that 2^ n >n for all n∈N.

Prove by the principle of mathematical induction that for all n in N : 1+4+7++(3n-2)=1/2n(3n-1)

Prove by the principal of mathematcal induction that for all n in N . 1^(2) + 3^(2) + 5^(2) + …… + (2n - 1)^(2) = (n(2n - 1) (2n + 1))/(3)

Using the principle of mathematical induction, prove that n<2^n for all n in N

Prove by the principle of mathematical induction that for all n in N ,n^2+n is even natural number.

Prove by the principle of mathematical induction that for all n in N ,n^2+n is even natural number.

Prove the following by using the principle of mathematical induction for all n in N : 1^2+3^2+5^2+dotdotdot+(2n-1)^2=(n(2n-1)(2n+1))/3

Prove the following by using the principle of mathematical induction for all n in N : 1 + 2 + 3 + ... + n <1/8(2n+1)^2 .

Prove by the principle of mathematical induction that for all n belongs to N :\ 1/(1. 3)+1/(3.5)+1/(5.7)++1/((2n-1)(2n+1))=n/(2n+1)

RD SHARMA ENGLISH-MATHEMATICAL INDUCTION-All Questions
  1. Let P(n) be the statement "3^n > n" . If P(n) is true, P(n+1) is also ...

    Text Solution

    |

  2. If P(n) is the statement n^2&gt; 100" , prove that whenever P(r) is...

    Text Solution

    |

  3. Prove by the principle of mathematical induction that for all n in N ...

    Text Solution

    |

  4. Prove by the principle of mathematical induction that for all n in N ...

    Text Solution

    |

  5. Prove by the principle of mathematical induction that: n(n+1)(2n+1) is...

    Text Solution

    |

  6. Prove by the principle of mathematical induction that for all n in N ...

    Text Solution

    |

  7. Prove that : cos^2alpha+cos^2(alpha+beta)-2cosalphacosbetacos(alpha+be...

    Text Solution

    |

  8. Prove that 1/(n+1)+1/(n+2)+...+1/(2n)> 13/24 ,for all natural number ...

    Text Solution

    |

  9. Prove the following by using the principle of mathematical inductio...

    Text Solution

    |

  10. Prove by induction the inequality (1+x)^ngeq 1+n x whenever x is pos...

    Text Solution

    |

  11. If P(n) is the statement n^3+n is divisible 3 is the statement P(3) tr...

    Text Solution

    |

  12. If P(n) is the statement n(n+1)(n+2) is divisible is 12 prove that the...

    Text Solution

    |

  13. Let P(n) be the statement 7 divides (2^(3n)-1)dot What is P(n+1)?

    Text Solution

    |

  14. If P(n) is the statement n(n+1) is even, then what is P(3)?

    Text Solution

    |

  15. If P(n) is the statement n^3+n is divisible by 3, prove that P(3) is t...

    Text Solution

    |

  16. If P(n) is the statement n^2+n is even, and if P(r) is true then P(r+1...

    Text Solution

    |

  17. If P(n) is the statement 2^ngeq3n , and if P(r) is true, prove that P(...

    Text Solution

    |

  18. Given an example of a statement P(n) such that it is true of all n ϵN.

    Text Solution

    |

  19. If P(n) is the statement n^2-n+41 is prime. Prove that P(1),\ P(2)a n ...

    Text Solution

    |

  20. Given an example of a statement P(n) which is true for all ngeq4 but P...

    Text Solution

    |