Home
Class 12
MATHS
For all ninNN, prove by principle of mat...

For all `ninNN`, prove by principle of mathematical induction that,
`(1)/(1*4)+(1)/(4*7)+(1)/(7*10)+ . . . ` to terms `=(n)/(3n+1)`.

Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

    SRISIRI PUBLICATION|Exercise 10.5 MAXIMA AND MINIMA - VSAQ . SAQ (SPQ)|1 Videos
  • DC'S & DR'S

    SRISIRI PUBLICATION|Exercise MISCELLANEOUS (3D MIS Q)|4 Videos

Similar Questions

Explore conceptually related problems

(1)/(1.3) + (1)/(3.5) + (1)/(5.7) + …. (n-3) terms

Using the principle of finite Mathematical Induction prove the following: (iii) 1/(1.4) + 1/4.7 + 1/7.10 + ……… + "n terms" = n/(3n+1) .

Prove by the method of induction, (1)/( 1.3) + (1)/( 3.5) + (1)/( 5.7) + . . . + (1)/( (2n - 1)(2n + 1)) = (n)/(2 n +1)

lim_(n to infty) ((1)/(3.7)+(1)/(7.11) +(1)/(11.15)+. . . +(n" terms ")) =

1+ 3+ 7 + 15… n terms =

Using the principle of finite Mathematical Indcution prove that 2.3 + 3.4 + 4.5 + ……."upto n terms" = (n(n^(2)+6n+11))/(3) .

If (1)/( 2 xx 4) + (1)/( 4 xx 6) + (1)/( 6 xx 8) + …. N terms = (kn)/( n+1) then k=

underset(n to oo)lim {(1)/(1.4)+(1)/(4.7)+(1)/(7.10)+....+(1)/((3n-2)(3n+1))}=

Using the principle of Mathematical Induction, show that 2.4^(2n+1)+3^(3n+1) is divisible by 11, forall n in N

Using the principle of finite Mathematical Induction prove that 1^(2)+(1^(2)+2^(2))+(1^(2)+2^(2)+3^(2)) + "n terms" = (n(n+1)^(2)(n+2))/(12), AA n in N .

SRISIRI PUBLICATION-BOARD MODEL PAPER-1-QUESTIONS
  1. IF overlinea,overlineb,overlinec are non-coplanar, then prove that the...

    Text Solution

    |

  2. Let overlinea=2overlinei+4overlinej-5overlinek,overlineb=overlinei+ove...

    Text Solution

    |

  3. IF overlinea=overlinei+2overlinej-3overlinekand overlineb=3overlinei-o...

    Text Solution

    |

  4. Prove that (cos 9^(@)+sin9^(@))/(cos9^(@)-sin9^(@)) = cot 36^(@).

    Text Solution

    |

  5. Find period of tan(x+4x+9x+…….n^(2)x).

    Text Solution

    |

  6. If sinhx=3" then show that "x=log(3+sqrt10)

    Text Solution

    |

  7. Show that |{:(bc,b+c,1),(ca,c+a,1),(ab,a+b,1):}|=(a-b)(b-c)(c-a)

    Text Solution

    |

  8. If ABCDEF is a regular hexagon with centre O , then P.T bar(AB)+bar(A...

    Text Solution

    |

  9. IF overlinea=overlinei-2overlinej-3overlinek,overlineb=2overlinei+over...

    Text Solution

    |

  10. If A is not an integral multiple of (pi)/(2), prove that (i) tan A +...

    Text Solution

    |

  11. Solve that following equations : 2cos^2theta+3sintheta=0

    Text Solution

    |

  12. Show that: cos(2tan^(-1)1/7)=sin(4^(-1)1/3)

    Text Solution

    |

  13. त्रिभुज ABC में , सिद्ध कीजिए कि tan ""(B-C)/(2)=(b-c)/(b+c)cot "...

    Text Solution

    |

  14. If f: A to B, g:B to C are two bijective functions then prove that gof...

    Text Solution

    |

  15. For all ninNN, prove by principle of mathematical induction that, (1...

    Text Solution

    |

  16. IF A=[{:(1,-2,3),(0,-1,4),(-2,2,1):}] than find (A')^-1.

    Text Solution

    |

  17. Solve the following system of equations by using Cramer,s ruel . 3x...

    Text Solution

    |

  18. If A=(1,-2,-1) , B=(4,0,-3),C= (1,2,-1),D=(2,-4,-5) then find distan...

    Text Solution

    |

  19. sin^2(A/2)+sin^2(B/2)-sin^2(C/2)=1-2cos(A/2)cos(B/2)sin(C/2)

    Text Solution

    |

  20. In a DeltaABC, If a=13 , b=14 , c=15, find R,r,r1,r2andr3.

    Text Solution

    |