Question

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

Answer 1

Refer to the attachment

Answer 2

n ∈ natural even numbers

Explanation:

1 + 3 + 5 + 7 + … + (2n-1)

• a = 1
• b = 2
• Uₙ = 2n - 1

sum of the first n terms :

Sₙ = n/2(a + Uₙ)

Sₙ = n/2(1 + 2n - 1)

Sₙ = n/2(2n)

Sₙ = n²

∴ so, the solution of n is all natural even numbers