Home
Class 11
MATHS
Prove by. mathematical induction :1.2+2....

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

Promotional Banner

Topper's Solved these Questions

  • MODEL QUESTION PAPERS-SET 7

    UNITED BOOK HOUSE|Exercise EXERCISE|50 Videos

  • MODEL QUESTION PAPERS-SET 9

    UNITED BOOK HOUSE|Exercise EXERCISE|48 Videos

Similar Questions

Explore conceptually related problems

Prove by mathematical induction. 1.1! + 2. 2! + 3. 3! + ... +n . n! = (n + 1)! - 1, where n ∈ 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 by mathematical induction 1^(2)+2^(2)+3^(2)+.....+(n+1)^(2)=((n+1)(n+2)(n+3))/(6)

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

By mathematical induction prove that, 1*2+2*2^(2)+3*2^(3)+ . . .+n*2^(n)=(n-1)*2^(n+1)+2,ninNN .

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: (3^(4n+1)+2^(2n+2)) is divisible by 7.

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 , 3^(2n+1)+2^(n+2) is divisible by 7, n in N

UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 8-EXERCISE
  1. If alphaand betaare positive acute angles and cos2alpha=(3cos2beta-1)/...

    Text Solution

    |

  2. In any triangle ABC If sinA : sinB: sinC=4:5:6,then prove that cos A ...

    Text Solution

    |

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

    Text Solution

    |

  4. If S1, S2 and S3 be respectively the sum of n, 2n and 3n terms of a G....

    Text Solution

    |

  5. Two parallel straight lines contains 5 points and 10 points respective...

    Text Solution

    |

  6. If the coefficients of 2nd,3rd and 4th terms in the (1+x)^(2n)are in A...

    Text Solution

    |

  7. Vertices of /\XYZ are X(-2, -3),Y (6, 1), and Z(1, 6). Find the co-ord...

    Text Solution

    |

  8. The equations of two sides of a square are 5x+12y-10=0 and 5x+12y+29=0...

    Text Solution

    |

  9. A circle passes through(1,-2) and (4,-3) and its.centre lies on the st...

    Text Solution

    |

  10. A point divides the line segment joining the point (2, -5. 8) and(3, 4...

    Text Solution

    |

  11. Show thatlim(xrarr0)(x^2sin(1/x))/(sinx)=0

    Text Solution

    |

  12. Differentiatesqrttanx,with respect to x.(With the help of 1st principl...

    Text Solution

    |

  13. Using contrapositive method show that the compound statement is are tr...

    Text Solution

    |

  14. If n is real and n > 3, show that n^2 > 9 (use the method of contradic...

    Text Solution

    |

  15. In a family, out of 3 children, one of them at least Boy. Find the por...

    Text Solution

    |

  16. If the variance of lst.n even natural numbers is 65, find the value of...

    Text Solution

    |

  17. Show thatsinalpha+sinbeta+singamma-sin(alpha+beta+gamma)=4sin ((alpha+...

    Text Solution

    |

  18. In /\ABCshow thata^3cos(B-C)+b^3cos(C-A)+c^3cos(A-B)=3abc

    Text Solution

    |

  19. Find the number of permutations and the number of combinations in the ...

    Text Solution

    |

  20. Solve :3x^2+(i-2)x-4i+10=0

    Text Solution

    |