Home
Class 11
MATHS
Prove that :1^2+2^2+3^2++n^2=(n(n+1)(2n+...

Prove that :`1^2+2^2+3^2++n^2=(n(n+1)(2n+1))/6`

Text Solution

AI Generated Solution

To prove that the sum of the squares of the first n natural numbers is given by the formula: \[ 1^2 + 2^2 + 3^2 + \ldots + n^2 = \frac{n(n+1)(2n+1)}{6} \] we will use the method of mathematical induction. ...
Promotional Banner

Topper's Solved these Questions

  • SINE AND COSINE FORMULAE AND THEIR APPLICATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|118 Videos
  • STATISTICS

    RD SHARMA|Exercise Solved Examples And Exercises|175 Videos

Similar Questions

Explore conceptually related problems

Prove the following by the principle of mathematical induction: 1^(2)+2^(2)+3^(2)++n^(2)=(n(n+1)(2n+1))/(6)

Prove that :1+2+3+...+n=(n(n+1))/(2)

Prove that 1^1*2^2*3^3....n^nle((2n+1)/3)^((n(n+1))/2) .

Prove that 1^(1)xx2^(2)xx3^(3)xx xx n^(n)<=[(2n+1)/3]^(n(n+1)/2),n in N

Prove that : 1^(3)+2^(3)+3^(3)++n^(3)={(n(n+1))/(2)}^(2)

Prove that 1+2+3+.....n=(n(n+1))/(2)

Prove that 2 + 4 + 6 + .... + 2n = n (n + 1)

Prove that: :2^(n)C_(n)=(2^(n)[1.3.5(2n-1)])/(n!)

Statement-1: 1^(2)+2^(2)+....+n^(2)=(n(n+1)(2n+1))/(6)"for all "n in N Statement-2: 1+2+3....+n=(n(n+1))/(2),"for all"n in N

RD SHARMA-SOME SPECIAL SERIES-Solved Examples And Exercises
  1. The sum of the series 2/3+8/9+(26)/(27)+(80)/(81)+ to n terms is n-1/2...

    Text Solution

    |

  2. Value of :1^3+2^3+3^3++n^3=

    Text Solution

    |

  3. Prove that :1^2+2^2+3^2++n^2=(n(n+1)(2n+1))/6

    Text Solution

    |

  4. Find the sum of the series 2^2+4^2+6^2+....+(20)^2

    Text Solution

    |

  5. Find the sum of nth term of this series and Sn denote the sum of its n...

    Text Solution

    |

  6. Sum the following series to n terms: 1/(1. 6)+1/(6. 11)+1/(11. 16)+1/(...

    Text Solution

    |

  7. Sum the following series to n terms: 1+4+13+40+121+

    Text Solution

    |

  8. Find the sum of all possible products of the first n natural numbers ...

    Text Solution

    |

  9. Sum of n terms the series : 1^2-2^2+3^2-4^2+5^2-6^2+

    Text Solution

    |

  10. Find the sum to n terms of the series: 1/(1+1^2+1^4)+2/(1+2^2+2^4)+...

    Text Solution

    |

  11. Sum the following series to n terms: 4+6+9+13+18+

    Text Solution

    |

  12. Find the sum : sum(r=1)^n1/((a r+b)(a r+a+b))

    Text Solution

    |

  13. Find the sum to n terms of the series: 3/(1^2 .2^2)+5/(2^2 .3^2)+7/(3...

    Text Solution

    |

  14. Sum the following series to n terms: 5+7+13+31+85+

    Text Solution

    |

  15. Find the sum to n terms of the series: 1/(1. 3)+1/(3. 5)+1/(5. 7)+

    Text Solution

    |

  16. Find the sum to n terms of the series: 3+9+15+35+63+

    Text Solution

    |

  17. Find the sum to n terms of the series: 1+5+12+22+35+

    Text Solution

    |

  18. Find the sum of the series: 1. n+2.(n-1)+3.(n-2)++(n-1). 2+n .1.

    Text Solution

    |

  19. Find the sum of series (3^3-2^3)+(5^3-4^3)+(7^3-6^3)+ upto 10 terms

    Text Solution

    |

  20. If Sn=sum(r=1)^n(1+2+2^2+ .......+2^r)/(2^r), then Sn is equal to (...

    Text Solution

    |