17. For which positive megets nis the ratio, abwe an integer - N EDUCATION om onts, where ka 0 anak el D. -1 7 9 Integer (A) odd only (B) even only (C) = 1 + 6k only, where k 20 andket (D)n = 1 + 3k, integer k20

For which positive integers n is the ratio (sum_(k=1)^(n)k^(2))/(sum_(k=1)^(n)k) an integer?

For which positive integers n is the ratio, (sum+(k=1)^(n) k^(2))/(sum_(k=1)^(n) k) an integer ?

For all positive integers k, if the greatest divisor of 25^k + 12k -1 is d , then 4sqrtd =

Prove that sum_(r=1)^(k) (-3)^(r-1) (3n)^C_(2r-1) = 0 , where k = 3n//2 and n is an even integer.

(x+1) is a factor of x^(n)+1 only if n is an odd integer (b) n is an even integer n is a negative integer (d) n is a positive integer

Prove that sum_(r=1)^(k) (-3)^(r-1) ""^(3n)C_(2r-1) = 0 , where k = 3n//2 and n is an even integer.

For the integer n, if n^(3) is odd,then which of the following statements are true? n is odd.II.n^(2) is odd.III.n^(2) is even (a) I only (b) II only (c) I and II only (d) I and III only

Consider the following statements: 1. a^n+b^n is divisible by a+b if n=2k+1, where k is a positive integer. 2. a^n-b^n is divisible by a-b if n=2k , where k is a positive integer. Which of the statements given above is /are correct? (a) 1 only (b) 2 only (c) both 1 and 2 (d) Neither 1 nor 2

If (12^(n)+1)backslash is divisible by 13, then n is (a) 1 only (b)12 only (c) any odd integer (d) any even integer

(x+1) is a factor of x^n+1 only if (a)n is an odd integer (b) n is an even integer (c )n is a negative integer (d)n is a positive integer