Question

For which positive integer n is the ratio $\frac { \sum _ { k = 1 } ^ { n } k ^ { 2 } } { \sum _ { k = 1 } ^ { n } k }$ an integer -

• A. Odd values of n only
• B. Even n only
• C. n = 6k +1 if k ³ 1 and kÎ I
• D. n = 3k + 1, k Î I, k ³ 0

Answer 1

Answer: (D)

n = 3k + 1, k Î I, k ³ 0

Answer 2

$\frac { \sum _ { k = 1 } ^ { n } k ^ { 2 } } { \sum _ { k = 1 } ^ { n } k }$ = , n = 3k + 1