Home
Class 11
MATHS
Prove by mathematical induction, 1+1/4+1...

Prove by mathematical induction, `1+1/4+1/9+...+1/n^2<2-1/n`when` n ge 2`, is a integer.

Promotional Banner

Topper's Solved these Questions

  • MODEL QUESTION PAPERS-SET 11

    UNITED BOOK HOUSE|Exercise EXERCISE|46 Videos
  • MODEL QUESTION PAPERS-SET 13

    UNITED BOOK HOUSE|Exercise EXERCISE|50 Videos

Similar Questions

Explore conceptually related problems

Prove by mathematical induction that 1/1.3+1/3.5+1/5.7+...+1/((2n-1)(2n+1)) = n/(2n+1),(n in N)

Prove by mathematical induction. 1/1.3+1/3.5+1/5.7+....+1/((2n-1)(2n+1))=n/(2n+1)

Prove by mathematical induction. 1.1! + 2. 2! + 3. 3! + ... +n . n! = (n + 1)! - 1, where n ∈ N .

Prove by mathematical induction, n.1+(n-1).2+(n-2).3+…+2.(n-1)+1.n = (n(n+1)(n+2))/6 where n in N .

Prove by mathematical induction that (11^(n+2)+12^(2n+1)) is divisible by 133 for all non-negative integers.

Prove by. mathematical induction : 1.2+2.2^2+3.2^3+...+n.2^n=(n-1)2^(n+1)+2,n in N

Prove that by mathematical induction, 4^n+15n-1 is divisible ny 9 when n in N .

Prove be mathematical induction : (1)/(3.6)+(1)/(6.9)+(1)/(9.12)+...+(1)/(3n(3n+3))=(n)/(9(n+1))

Prove that by mathematical induction : 3^(2n+ 2) - 8n - 9 is divisible by 64 where 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 .

UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 12-EXERCISE
  1. If tan^2 alpha = 1 + 2 tan^2 beta, show that cos2 beta = 1 + 2cos 2alp...

    Text Solution

    |

  2. Solve :sin x 4 cos x = sin 2x 4 cos 2x.

    Text Solution

    |

  3. Prove by mathematical induction, 1+1/4+1/9+...+1/n^2<2-1/nwhen n ge 2,...

    Text Solution

    |

  4. If arg ((z-1)/(z+1))=pi/4,, then show that in complex plane, the locus...

    Text Solution

    |

  5. Find the term independent of x of the expansion of (1+x)^3(x-1/x)^6

    Text Solution

    |

  6. If pth, qth and rth terms of on AP are a. b and c, then show that a(q...

    Text Solution

    |

  7. A straight line form a right angled triangle with the axes. If the len...

    Text Solution

    |

  8. If the co-ordinate of vertices of a triangle are (10, 4), (-4, 9) and ...

    Text Solution

    |

  9. Find the co-ordinate of a point on the circle x^2 +y^2 - 4x + 2y - 20...

    Text Solution

    |

  10. The co-ordinate of the vertices of a triangle are A(0, 2, -3), B(- 2,...

    Text Solution

    |

  11. Differentiate x+1/x(x!=0)at x = 1, with respect to x, with the help of...

    Text Solution

    |

  12. Evaluate : lim(xrarr0)sin(x^2+4x)/(x^3-5x^2+2x)

    Text Solution

    |

  13. ‘If p' and q are rational numbers, then pq is also rational convert t...

    Text Solution

    |

  14. ‘Square of a whole number is positive or negative’-find the validity o...

    Text Solution

    |

  15. If two numbers a and b are-chosen at random from the 1st 30 natural nu...

    Text Solution

    |

  16. Find A.M. and SD of the following distribution table :

    Text Solution

    |

  17. Using vector method in a triangle , prove that, (i) a/(sinA)=b/(sinB...

    Text Solution

    |

  18. If alpha,beta positive acute angles and sec(alpha+beta)-sec(alpha-beta...

    Text Solution

    |

  19. Draw the graph and find the common region of the system of following i...

    Text Solution

    |

  20. if z1=1+isqrt3,z2=sqrt3-ishow that (a)arg (z1z2)=arg(z1)+arg(z2)and (b...

    Text Solution

    |