lim-n-a-2a-na-n-2-where-a-R-and-x-is-the-floor-of-x-R- Tinku Tara March 15, 2024 Limits 0 Comments FacebookTweetPin Question Number 205307 by universe last updated on 15/Mar/24 limn→∞⌊a⌋+⌊2a⌋+…+⌊na⌋n2wherea∈Rand⌊x⌋isthefloorofx∈R Commented by Frix last updated on 15/Mar/24 Justguessing:−∞fora<0a2fora⩾0 Answered by Mathspace last updated on 15/Mar/24 [a]⩽a<[a]+1⇒[a]⩽aeta−1<[a]⇒a−1<[a]⩽aka−1<[ka]⩽ka⇒∑k=1n(ka−1)<∑k=1n[ka]⩽∑k=1nka⇒a.n(n+1)2−n<∑k=1n[ka]⩽an(n+1)2⇒n(n+1)n2a−1n<∑k=1n[ka]n2⩽n(n+1)2n2aonalimn→+∞n(n+1)2n2a−1n=a2limn→+∞n(n+1)a2n2=a2⇒limn→+∞∑k=1n[ka]n2=a2 Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: Question-205302Next Next post: Question-205306 Leave a Reply Cancel replyYour email address will not be published.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.