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

`1^(2)+2^(2)+3^(2)+..........+n^(2)=(n(n+1)(2n+1))/(6)`

Promotional Banner

Topper's Solved these Questions

  • SOLVED PAPER 2019-2

    OSWAAL PUBLICATION|Exercise EXERCISE|57 Videos

  • SOLVED PAPER 2020-2

    OSWAAL PUBLICATION|Exercise EXERCISE|59 Videos

Similar Questions

Explore conceptually related problems

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

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)

The sum of first n terms of the series 1^(2) + 2.2^(2) +3^(2) + 2. 4^(2) + 5^(2) + 2. 6^(2) + "........." is ( n ( n + 1)^(2))/( 2) when n is even. When, n is odd, the sum is :

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)

1^(2) + 1+ 2^(2) + 2 + 3^(2) + 3+"............"+n^(2) + n is equal to :

Prove that by using the principle of mathematical induction for all n in N : 1.2+ 2.2^(2)+ 3.2^(3)+ ....+ n.2^(n)= (n-1)2^(n+1)+2

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

lim_(n rarr oo) { n/(n^(2)+1^(2)) + n/(n^(2)+2^(2))+......+ n/(n^(2)+n^(2))} is equal to

Prove that by using the principle of mathematical induction for all n in N : 1.2.3+ 2.3.4+ ....+ n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/(4)

OSWAAL PUBLICATION-SOLVED PAPER 2020-1-EXERCISE
  1. A committee of two persons is selected from two men and two women. Wha...

    Text Solution

    |

  2. A committee of two persons is selected from two men and two women. Wha...

    Text Solution

    |

  3. A committee of two persons is selected from two men and two women.What...

    Text Solution

    |

  4. If E and F are two events such that P(E)=1/4, P(E)=1/2 and P(E and F)=...

    Text Solution

    |

  5. If E and F are two events such that P(E)=1/4, P(E)=1/2 and P(E and F)=...

    Text Solution

    |

  6. Define a modulus function . Draw its graph. Also write down its domai...

    Text Solution

    |

  7. 1^(2)+2^(2)+3^(2)+..........+n^(2)=(n(n+1)(2n+1))/(6)

    Text Solution

    |

  8. Prove that cos^(2)+x+cos^(2) (x+pi/3)+cos^(2)(x-pi/3)=3/2 and hence fi...

    Text Solution

    |

  9. Solve the following system of inequalities graphically x+2yle8,2x+yle8...

    Text Solution

    |

  10. A group consists of 5 girls and 7 boys.In how many ways can a team of ...

    Text Solution

    |

  11. A group consists of 4 girls and 7 boys. In how many ways can a team of...

    Text Solution

    |

  12. State and prove Bionomial theorem for any positive integer n.

    Text Solution

    |

  13. Derive the equation of a plane in normal form both in the vector and C...

    Text Solution

    |

  14. Prove that lim(thetararr0)(sin theta)/(theta)=1.

    Text Solution

    |

  15. Derive the formula to find the co-ordinates of a point which divide th...

    Text Solution

    |

  16. Find the mean deviation about median for the following data:

    Text Solution

    |

  17. (a)Derive geometrically that cos(x+y)=cos x cos y-sin x sin y.Hence de...

    Text Solution

    |

  18. (b) Find the sum to n terms of the series 1 xx 2 xx 3 + 2 xx 3 xx 4 + ...

    Text Solution

    |

  19. Derive the equation of the ellipse in the form (x^(2))/(a^(2))+(y^(2))...

    Text Solution

    |

  20. (b) Find the derivative of (x^(5) - cos x)/(sin x) with respect to x.

    Text Solution

    |