Question

Ind all natural numbers n such that 1+3+5+7+...+(2n-1) sum is divisible by 4

Answer 1

• All even natural numbers

Explanation:

This is an AP with:

• The first term = 1
• Number of terms = n
• Common difference = 2

Find the sum of the first n terms:

• 
  `S_n= n(1+2n-1)/2=n^2`

The sum is divisible by 4 if n is even number:

• n = 2k ⇒ n² = 4k² ≡ 0 mod 4