MAD101_-_Test2_-_SU_2024_2075.webp

Question: 55
(Choose 1 answer)
(See picture)
A. (i)
B. (ii)
C. (iii)
D. (iv)
Given that 1^{3}+2^{3}+...+n^{3}=(n(n+1)/2)^{2} for all n\ge1
Which of the following equations is true?
(i) 1^{3}+...+(k+1)^{3}=(k(k+1)/2)^{2}+k^{3}
(ii) 1^{3}+...+(k+1)^{3}=(k(k+1)/2)^{2}+(k+1)^{3}
(iii) 1^{3}+...+(k+1)^{3}=(k(k-1)/2)^{2}+(k+1)^{3}
(iv) 1^{3}+...+(k+1)^{3}=(k(k-1)/2)^{2}+k^{3}