If-k-is-odd-then-show-that-1-k-2-k-3-k-n-k-is-divisible-by-1-2-3-n-for-every-n-N-

Tinku Tara June 4, 2023 Arithmetic 0 Comments

Question Number 46460 by Tawa1 last updated on 26/Oct/18

If k is odd, then show that 1^k + 2^k + 3^k + ... + n^k is divisible by 1 + 2 + 3 + ... + n, for every n ∈ N

$$\mathrm{If}\:\:\mathrm{k}\:\mathrm{is}\:\mathrm{odd},\:\mathrm{then}\:\mathrm{show}\:\mathrm{that}\:\:\:\:\mathrm{1}^{\mathrm{k}} \:+\:\mathrm{2}^{\mathrm{k}} \:+\:\mathrm{3}^{\mathrm{k}} \:+\:…\:+\:\mathrm{n}^{\mathrm{k}} \:\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\:\: \\ $$$$\mathrm{1}\:+\:\mathrm{2}\:+\:\mathrm{3}\:+\:…\:+\:\mathrm{n},\:\:\:\:\:\mathrm{for}\:\mathrm{every}\:\:\:\mathrm{n}\:\in\:\mathrm{N} \\ $$

Facebook Tweet Pin

If-k-is-odd-then-show-that-1-k-2-k-3-k-n-k-is-divisible-by-1-2-3-n-for-every-n-N-

Leave a Reply Cancel reply