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The sum of the cubes of first n natural ...

The sum of the cubes of first n natural numbers is -

A

`n^(3)`

B

`(n(n+1))/(2)`

C

`(1)/(6)n(n+1)(2n+1)`

D

`[(n(n+1))/(2)]^(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
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CHHAYA PUBLICATION-MATHEMATICAL INDUCTION -Exercise
  1. The sum of first n numbers is -

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  2. The sum of the squares of first n natural numbers is -

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  3. The sum of the cubes of first n natural numbers is -

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  4. State which of the following statement is true ?

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  5. If (2^(2n)-1) is divisible by 3, then show that, [2^(2(n+1))-1] is als...

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  6. If (2^(3n)-1) is divisible by 7, then prove that, [2^(3(n+1))-1] is al...

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  7. If 1*1!+2*2!+3*3!+ . . .+n*n ! =(n+1)!-1 then show that, 1*1!+2*2!+3*3...

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  8. If (10^(2n-1)+1) is divisible by 11, then prove that (10^(2n+1)+1) is ...

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  9. If (15^(2n-1)+1) is divisible by 16, then show that (15^(2n+1)+1) is a...

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  10. If [12^(n)+25^(n-1)] is divisible by 13, then show that [12^(n+1)+25^(...

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  11. If [n^(3)+(n+1)^(3)+(n+2)^(3)] is also divisible by 9. then show that,...

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  12. If ninN,xgt-1 and (1+x)^(n)ge1+nx, then prove that (1+x)^(n+1)ge1+(n+1...

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  13. Let f(n)=n(n+1)(2n+1), if f(n) is always divisible ny 6 then prove tha...

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  14. For all ninNN, prove by principle of mathematical induction that, 1+...

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  15. For all ninNN, prove by principle of mathematical induction that, a+...

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  16. For all ninNN, prove by principle of mathematical induction that, si...

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  17. For all ninNN, prove by principle of mathematical induction that, si...

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  18. For all ninNN, prove by principle of mathematical induction that, (c...

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  19. For all ninNN, prove by principle of mathematical induction that, (1...

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  20. For all ninNN, prove by principle of mathematical induction that, a+...

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