Home
Class 11
MATHS
Prove that, 1^2 + 2^2 + …..+ n^2 gt (n^3...

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

Promotional Banner

Topper's Solved these Questions

  • PRINCIPLE OF MATHEMATICAL INDUCTION

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

    KUMAR PRAKASHAN|Exercise NCERT EXEMPLAR PROBLEMS (LONG ANSWER TYPE QUESTIONS)|8 Videos
  • PRINCIPLE OF MATHEMATICAL INDUCTION

    KUMAR PRAKASHAN|Exercise TEXTBOOK BASED MCQS|10 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

For all n gt= 1 , prove that, 1^2 + 2^2 + 3^2 + 4^2 + …….+n^2 = (n(n+1)(2n+1))/(6)

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

Prove that (n!) (n + 2) = [n! + (n + 1)!]

By using the principle of mathematical induction , prove the follwing : P(n) : (2n + 7) lt (n+3)^2 , n in N

By using the principle of mathematical induction , prove the follwing : P(n) : 2 + 4+ 6+ …..+ 2n =n(n+1) , n in N

P(n) : 1^(2) + 2^(2) + 3^(2) + .......+ n^(2) = n/6(n+1) (2n+1) n in N is true then 1^(2) +2^(2) +3^(2) + ........ + 10^(2) = .......

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

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)

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)

Prove that .^(n-1)C_(3)+.^(n-1)C_(4) gt .^(n)C_(3) if n gt 7 .