For and odd integer n ge 1, n^(3) - (n -...

For and odd integer `n ge 1, n^(3) - (n - 1)^(3) ` + ……
`+ (- 1)^(n-1) 1^(3)`

A

`1/2(n-1)^2(2n-1)`

B

`1/4(n-1)^2(2n-1)`

C

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

D

`1/4(n+1)^2(2n-1)`

Verified by Experts

The correct Answer is:

D

Similar Questions

Explore conceptually related problems

For a positive integer n , let a(n) = 1+ 1/2 + 1/3 +…+ 1/(2^(n)-1) : Then

If n is an odd integer then n ^(2) -1 is divisible by

If n is an odd integer greater than or equal to 1, then the value of n^(3)-(n-1)^(3)+(n-1)^(3)-(n-1)^(3)+...+(-1)^(n-1)1^(3)

For every integer n>=1,(3^(2^(n))-1) is divisible by

Prove that (1+i)^(2n)+(1-i)^(2n) = 0 if n is an odd integer and, equal to 2^(n+1)/((-1)^(n//2) if n is an even integer.

If (n-1) is an odd number, what are the two other odd numbers nearest to it? n , n -1 (b) n , n , - 2 n 3, n + 1 (d) n 3, n + 5