neopang neopang
  • 09-10-2021
  • Mathematics
contestada

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

Respuesta :

mhanifa
mhanifa mhanifa
  • 09-10-2021

Answer:

  • All even natural numbers

Step-by-step 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:

  • [tex]S_n= n(1+2n-1)/2=n^2[/tex]

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

  • n = 2k ⇒ n² = 4k² ≡ 0 mod 4
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