Home
Class 11
MATHS
1+2+3+…….+(n+1)= ((n+1) (n+2))/(2) , n i...

`1+2+3+…….+(n+1)= ((n+1) (n+2))/(2) , n in N`.

A

For P(1) , L.H.S = 7 = R.H.S.

B

For P(1) , L.H.S = 3 = R.H.S.

C

`P(k) rArr P(k+1) , k in N` is not true

D

By the principle of mathematical induction P(n) is true for all `n in N` . Which is not true .

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    KUMAR PRAKASHAN|Exercise TEXTBOOK ILLUSTRATIONS FOR PRATICE WORK|8 Videos
  • PRINCIPLE OF MATHEMATICAL INDUCTION

    KUMAR PRAKASHAN|Exercise NCERT EXEMPLAR PROBLEMS (SHORT ANSWER TYPE QUESTIONS)|16 Videos
  • PRINCIPLE OF MATHEMATICAL INDUCTION

    KUMAR PRAKASHAN|Exercise PRACTICE WORK|20 Videos
  • PERMUTATIONS AND COMBINATIONS

    KUMAR PRAKASHAN|Exercise PRACTICE WORK |40 Videos
  • PROBABILITY

    KUMAR PRAKASHAN|Exercise PRACTICE WORK|40 Videos

Similar Questions

Explore conceptually related problems

By using the principle of mathematical induction , prove the follwing : P(n) : (1)/(1.2) + (1)/(2.3) + (1)/(3.4) + …….+ (1)/(n(n+1)) = (n)/(n+1) , n in N

By using the principle of mathematical induction , prove the follwing : P(n) : 1/2 + 1/4 + 1/8 + ……..+ (1)/(2^n) = 1 - (1)/(2^n) , n in N

Prove that, 1^2 + 2^2 + …..+ n^2 gt (n^3)/(3) , n in N

By using the principle of mathematical induction , prove the follwing : (1)/(1.4) + (1)/(4.7) + (1)/(7.10) + ………..+ (1)/((3n - 2)(3n+1)) = (n)/(3n + 1) , n in N

By using the principle of mathematical induction , prove the follwing : 1 + (1)/(1+2) + (1)/(1+2+3) + …..+ (1)/(1+2+…..+n) = (2n)/(n+1) , n in N

Prove the following 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)

By using the principle of mathematical induction , prove the follwing : P(n) : 1^2 + 2^2 + 3^2+…………+n^2 = n/6 (n+1) (2n+1), n in N

If S_(n)=1 + (1)/(2) + (1)/(2) + …..+ (1)/(2^(n-1)), (n in N) then …….

Show that, (1 xx 2^(2) + 2 xx 3^(2) + ….+ n xx (n+1)^(2))/(1^(2) xx 2 + 2^(2) xx 3 + ….+ n^(2) xx (n+1))= (3n+ 5)/(3n+ 1)

Using mathematical induction , show that (1-(1)/(2^2))(1-(2)/(3^2))(1-(1)/(4^2)).....(1-(1)/((n+1)^2))=(n+2)/(2(n+1)), forall n in N .