Home
Class 11
MATHS
Use mathematical induction to prove that...

Use mathematical induction to prove that statement `1^(3) + 2^(3) + 3^(3) + . . . + n^(3) = (n^(2) (n + 1)^(2))/( 4) , AA n in N`

Text Solution

Verified by Experts

The correct Answer is:
`1^(3) + 2^(3) + 3^(3) + . . . + n^(3) = (n^(2) (n + 1)^(2))/(4)` is true for all `n in N `
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL INDUCTION

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise Exercise 2 (a)|15 Videos

  • MARCH - 2016 (TELANGANA)

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise Section -C (Long answer type quesitons)|7 Videos

  • MATRICES

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise SOLVED PROBLEMS |45 Videos

Similar Questions

Explore conceptually related problems

Use mathematical induction to prove that statement sum_(k = 1)^(n) (2 K - 1)^(2) = (n (2 n - 1) (2n + 1))/( 3) for all n in N

Use mathematical induction to prove that 2 n - 3 le 2^(n-2) for all n ge 5, n in N

If 2^(3) + 4^(3) + 6^(3) + … + (2n)^(3) = kn^(2) ( n+1)^(2) then k=

S_(n) = 1^(3) + 2^(3) + 3^(3) + …... + n^(3) and T_(n) = 1+ 2 + 3+ 4…...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 .

Using Mathematical Induction, prove that statement for all n in N 1.2.3+2,3,4+……….+("upto n terms")=(n(n+1)(n+2)(n+3))/(4) .

Using Mathematical Induction, prove that statement for all n in N (1+3/1)(1+5/4)(1+7/9)........(1+(2n+1)/n^2)=(n+1)^2 .

Using the principle of finite Mathematical Induction prove that 1.2.3+2.3.4+3.4.5.+………… upto n terms = n(n+1)(n+2)(n+3))/4,for all 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,foralln in N