Home
Class 11
MATHS
For all n ge 1 prove that 1^(2)+2^(2)+...

For all `n ge 1` prove that
`1^(2)+2^(2)+ 3^(2)+4^(2)+….+n^(2)= (n(n+1)(2n+1))/(6)`

Promotional Banner

Topper's Solved these Questions

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    NCERT BANGLISH|Exercise EXERCISE - 4.1|24 Videos
  • PERMUTATIONS AND COMBINATIONS

    NCERT BANGLISH|Exercise Miscellaneous Exercise on Chapter 7|11 Videos
  • PROBABILITY

    NCERT BANGLISH|Exercise MISCELLANEOUS EXERCISEON CHAPTER 25|1 Videos

Similar Questions

Explore conceptually related problems

Prove that 1^(2) +2^(2)+ ….+n^(2) gt (n^(3))/(3) n in N

For all n ge 1 prove that (1)/(1.2)+ (1)/(2.3)+(1)/(3.4)+.....+(1)/(n(n+1))=(n)/(n+1)

Using the principle of mathematical induction, prove that 1.3 + 2.3^(2) + 3.3^(2) + ... + n.3^(n) = ((2n-1)(3)^(n+1)+3)/(4) for all n in N .

Prove by mathematical induction that, 1^(2)-2^(2)+3^(2)-4^(2)+ . . .. +(-1)^(n-1)*n^(2)=(-1)^(n-1)*(n(n+1))/(2),ninNN .

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

If n is a positive integer, show that, (n+1)^(2) + (n+2)^(2) + …+ 4n^(2) = (n)/(6)(2n+1)(7n+1)

By ........in "Principle of Mathematical Induction" prove that for all n in N 1^2+2^2+3^2+.......+n^2=(n(n+1)(2n+1))/(6)

By principle of mathematical induction,prove that 1^(3)+2^(3)+3^(3)+ . . .. +n^(3)=[(n(n+1))/(2)]^(2) for all ninNN

Applying the principle of mathematical induction (P.M.I.) prove that 1^2+2^2+3^2+.......+n^2=(n(n+1)(2n+1))/6

Prove that by using the principle of mathematical induction for all n in N : 1.3+ 2.3^(2)+ 3.3^(3)+ ....+ n.3^(n)= ((2n-1)3^(n+1)+3)/(4)

NCERT BANGLISH-PRINCIPLE OF MATHEMATICAL INDUCTION-EXERCISE - 4.1
  1. For all n ge 1 prove that 1^(2)+2^(2)+ 3^(2)+4^(2)+….+n^(2)= (n(n+1)...

    Text Solution

    |

  2. Prove that by using the principle of mathematical induction for all n...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. Prove that by using the principle of mathematical induction for all n...

    Text Solution

    |

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

    Text Solution

    |

  7. Prove that by using the principle of mathematical induction for all n...

    Text Solution

    |

  8. Prove that by using the principle of mathematical induction for all n...

    Text Solution

    |

  9. Prove that by using the principle of mathematical induction for all n...

    Text Solution

    |

  10. Prove that by using the principle of mathematical induction for all n...

    Text Solution

    |

  11. Prove that by using the principle of mathematical induction for all n...

    Text Solution

    |

  12. Prove that by using the principle of mathematical induction for all n...

    Text Solution

    |

  13. Prove that by using the principle of mathematical induction for all n...

    Text Solution

    |

  14. Prove that by using the principle of mathematical induction for all n...

    Text Solution

    |

  15. Prove that by using the principle of mathematical induction for all n...

    Text Solution

    |

  16. Prove that by using the principle of mathematical induction for all n...

    Text Solution

    |

  17. Prove that by using the principle of mathematical induction for all n...

    Text Solution

    |

  18. Prove that by using the principle of mathematical induction for all n...

    Text Solution

    |

  19. Prove that by using the principle of mathematical induction for all n...

    Text Solution

    |

  20. Prove that by using the principle of mathematical induction for all n...

    Text Solution

    |

  21. Prove that by using the principle of mathematical induction for all n...

    Text Solution

    |