Question-if-k-is-odd-amp-A-1-k-2-k-n-k-amp-B-1-2-n-prove-that-B-A- Tinku Tara June 4, 2023 Algebra 0 Comments FacebookTweetPin Question Number 192425 by mehdee42 last updated on 17/May/23 Questionif“k″isodd&A=1k+2k+…+nk&B=1+2+…+nprovethat:B∣A Answered by MM42 last updated on 24/May/23 Wekhnow;1+2+…+n=n(n+1)2&(n,n+12)=1or(n2,n+1)=1Thus,itsofficestoshowthatn∣A&n+12∣Aorn2∣A&n+1∣Aproof∴if“n″iseven⇒n2∣1k+(n−1)k,2k+(n−2)k,…(i)n+1∣1k+nk,2k+(n−1)k,…(ii)(i),(ii)⇒B∣Aif“n″isodd⇒n∣1k+(n−1)k,2k+(n−2)k,…(iii)n+12∣1k+nk,2k+(n−1)k,…(iv)(iii),(iv)⇒B∣A⇒∀n∈N⇒1+2+3+…+n∣1k+2k+…+nk;if“k″is“odd″ Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: log-10-10-Next Next post: Question-126895 Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.