Home
Class 11
MATHS
If P(n)=2+4+6+…..+2n ninN then P(k) =k(k...

If `P(n)=2+4+6+…..+2n` `ninN` then `P(k) =k(k+1)` `implies` `P(k+1)=(k+1)(k+2)` for all `kinN`. So we can conclude that `P(n)=n(n+1)` for:

A

All`ninN`

B

`ngt1`

C

`ngt2`

D

Nothing can be said

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • BASIC MATHEMATICS

    PATHFINDER|Exercise QUESTION BANK |266 Videos

  • BINOMIAL THEOREM AND PRINCIPLE OF MATHEMATICAL INDUCTION

    PATHFINDER|Exercise QUESTION BANK|68 Videos

Similar Questions

Explore conceptually related problems

If .^(n)C_(3)=k.n(n-1)(n-2) then k=

A sequence b_(0),b_(1),b_(2), . . . is defined by letting b_(0)=5 and b_(k)=4+b_(k-1) , for all natural number k. Show that b_(n)=5+4n , for all natural number n using mathematical induction.

If a_k=1/(k(k+1)) for k=1 ,2……..,n then prove that (sum_(k=1)^n a_k)^2 =n^2/(n+1)^2

Let P(n) denote the statement that n^2+n is odd. It is seen that P(n) implies P(n+1) , P(n) is true for all

Let P(n) be the statement : 2^(n)gt3n . IF P(m) is true, show that, P(m+1) is true. Do you conclude that, P(n) is true for all ninNN ?

sum_(k=1)^ook(1-1/n)^(k-1) =?

For what value of k are the points (k ,2-2k)(-k+1,2k)a n d(-4-k ,6,6-2k) are collinear?

if underset(k=1)oversetnsum(k^2+1)k! =1999xx2000! then prove that n=1999

If p inNN then the expression p^(n+1)+(p+1)^(2n-1) is divisible by the expressions are -

If k in R_o then det{adj(k I_n)} is equal to (A) K^(n-1) (B) K^((n-1)n) (C) K^n (D) k

PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
  1. The value of where ^nCr is

    Text Solution

    |

  2. If the sum of odd numbered terms and the sum of even numbered terms in...

    Text Solution

    |

  3. If P(n)=2+4+6+…..+2n ninN then P(k) =k(k+1) implies P(k+1)=(k+1)(k+2) ...

    Text Solution

    |

  4. The value of the natural numbers n such that the inequality 2^ngt2n+1 ...

    Text Solution

    |

  5. When P is a natural number then p^(n+1)+(p+1)^(2n-1) is divisible by

    Text Solution

    |

  6. Let P(n) denote the statement that n^2+n is odd. It is seen that P(n) ...

    Text Solution

    |

  7. For a positive integer n let a(n)=1+1/2+1/3+1/4+….+1/((2^n)-1) Then

    Text Solution

    |

  8. Let S(k) =1+3+5+……+(2k-1)=3+k^2 Then which of the following is true:

    Text Solution

    |

  9. Statement-1 for every natural number nge2 1/sqrt1 +1/sqrt2 +…..+1/sqrt...

    Text Solution

    |

  10. (1+x)^n-nx-1 is divisible by (where n in N)

    Text Solution

    |

  11. Statement-1 : 11^(25) +12^(25) when divided by 23 leaves the remainder...

    Text Solution

    |

  12. The coefficient of x^(53) in the expansion of sum(m=0)^(100) ^100Cm(x-...

    Text Solution

    |

  13. The coefficient of y in the expansion of (y^2+(c/y))^5 is

    Text Solution

    |

  14. The term independent of x in (x^2-(1/x))^9 is

    Text Solution

    |

  15. The coefficients of x^p and x^q in the expansion of (1+x)^(p+q) are

    Text Solution

    |

  16. If x^m occurs in the expansion of (x+(1/x^2))^(2n) then the coefficien...

    Text Solution

    |

  17. Sum of the series 2C0+C1/2 2^2 +C2/3 2^3+………+Cn/(n+1) 2^(n+1)

    Text Solution

    |

  18. The value of nC0. ^nCn +^nC1 . ^nC(n-1)++……..+^nCn . ^nC0

    Text Solution

    |

  19. If (1+x)^(15)=C0+C1x+C2x^2+……..+C(15)x^(15) then ,^15C0^2-^15C1^2+^15C...

    Text Solution

    |

  20. If sn= sum(r=0)^n 1/(^"nCr) and tn=sum(r=0)^n r/("^nCr) then tn/sn is ...

    Text Solution

    |